Research and Publications

Books

• MacKay, R. S. and J.D. Meiss, Eds. (1987). Hamiltonian Dynamical Systems: a reprint selection. London, Adam-Hilgar Press, 784pp., ISBN 0-85274-205-3. (Buy from Amazon)
• Hazeltine, R. D. and J.D. Meiss (1991). Plasma Confinement. Redwood City, CA, Addison-Wesley, 394 pp., ISBN 0201-53353-5.
• R.D. Hazeltine and J.D. Meiss, Plasma Confinement, (2003) 2nd Edition, Dover Press, 480 pp., ISBN 0486432424. (Buy from Amazon)
• J.D. Meiss, Differential Dynamical Systems, (2007) SIAM, Philadelphia 412 pp., ISBN 978-0-899816-35-1.
• Meiss, J.D., Differential Dynamical Systems: Revised Edition. (2017) SIAM, Philadelphia, 392 pp., ISBN 978-1-61197-463-8.

Pedagogical Articles

• J.D. Meiss, Symplectic Maps, Variational Principles, and Transport, Reviews of Modern Physics 64 795-848 (1992) (reprint)
• J.D. Meiss, Hamiltonian Systems, Symplectic Maps, and The Standard Map, articles in the Encyclopedia of Nonlinear Science, ed. Alwyn Scott. (New York, Routledge) (2005). ISBN: 1-57958-385-7
• J.D. Meiss, Dynamical systems, Scholarpedia 2(2):1629 (2007).
• J.D. Meiss, Hamiltonian systems, Scholarpedia 2(8):1943 (2007).
• J.D. Meiss, "Visual Explorations of Dynamics: the Standard Mapping", Pramana, Indian Academy of Sciences, 70 965-988(2008) (arXiv preprint), (Corrected reprint).
• J.D. Meiss, "Thirty Years of Turnstiles and Transport", Chaos 25(9): 097602 (2015) ( arXiv preprint)
• J.D. Meiss, "Ordinary Differential Equations", The Princeton Companion to Applied Mathematics. pp 181-190 (2015)
• J.D. Meiss "Integrability, Anti-Integrability and Volume-Preserving Maps", CMS Notes 14(4) 13-14 (2015)

Fields of Research

Computational Topology

• V. Robins, J.D. Meiss, and E. Bradley, "Computing Connectedness: an exercise in computational topology", Nonlinearity 11 913-922 (1997). (PS Preprint).
• V. Robins, J.D. Meiss, and L. Bradley, "Computing Connectedness: Disconnectedness and Discreteness", Phys. D 139 276-300 (1999). (PDF reprint),
• Z. Alexander, J.D. Meiss, E. Bradley, and J. Garland, "Iterated Function System Models in Data Analysis: Detection and Separation", Chaos 22 023103 (2102) . (Preprint).
• Z. Alexander, E. Bradley, J.D. Meiss, and N. Sanderson, "Simplicial Multivalued Maps and the Witness Complex for Dynamical Analysis of Time Series", SIAM J. Appl. Dyn. Sys. 14(3): 1278-1307. (ArXiv Preprint).
• J. Garland, E. Bradley and J.D. Meiss, "Exploring the Topology of Dynamical Reconstructions", (ArXiv Preprint).
• Deshmukh, V., T.E. Berger, E. Bradley, and J.D. Meiss, "Leveraging the Mathematics of Shape for Solar Magnetic Eruption Prediction", J. Space Weather and Space Climate 10: 13 (2020). (arXiv Preprint)
• Deshmukh, V., V., E. Bradley, J. Garland, J.D. Meiss, "Using Curvature to Select the Time Lag for Delay Reconstruction", Chaos 30(6) 063143 (2020). (arXiv Preprint)
• Deshmukh, V., T. Berger, J.D. Meiss and E. Bradley "Shape-based Feature Engineering for Solar Flare Prediction", Thirty-Third AAAI Conference on Innovative Applications of Artificial Intelligence, IAAI Jan 2021 . (ArXiv Preprint)
• Deshmukh, V., E. Bradley, J. Garland, J.D. Meiss "Towards automated extraction and characterization of scaling regions in dynamical systems", Chaos 31(12) 123102 (2021). (ArXiv Preprint)
• Deshmukh,V. R. Meikle, E. Bradley, J.D. Meiss, and J. Garland "Using scaling-region distributions to select embedding parameters", Physica D, 446, 133674 2023 (ArXiv Preprint )
• Deshmukh, V., S. Baskar, T.E. Berger, E. Bradley, and J.D. Meiss, "Comparing Feature Sets and Machine Learning Models for Prediction of Solar Flares:Topology, Physics, and Model Complexity", "Astron & Astrophys in press (2023) (ArXiv Preprint )

Fluid Dynamics

• P. Mullowney, K. Julian and J.D. Meiss, "Blinking rolls: chaotic advection in a 3D flow with an Invariant", SIAM J. Appl. Dyn. Sys. 4 159-186 (2005). (PDF reprint)
• P. Mullowney, K. Julien, and J.D. Meiss, "Chaotic Advection in the Küppers-Lortz State", Chaos 18 033104 (2008). (arXiv preprint)
• B.A. Mosovsky, M.F.M. Speetjens, and J.D. Meiss, "Finite-Time Transport in Volume-Preserving Flows", Phys. Rev. Lett 110(21) 214101 (2013)
• R.M. Neupauer, J.D. Meiss, and D.C. Mays "Chaotic advection and reaction during engineered injection and extraction in heterogeneous porous media", Water Resources Research 50 WR014057 (2014).
• K.R. Pratt, J.D. Meiss, and J.P. Crimaldi, "Reaction Enhancement of Initially Distant Scalars by Lagrangian Coherent Structures", Phys. Fluids 27 035106 (2015). (Preprint).
• Mitchell, R.A., and J.D. Meiss, "Designing a Finite-Time Mixer: Optimizing Stirring for Two-Dimensional Maps." SIAM J. Dyn. Sys. 16(3), 1514-1542 (2017). (arXiv Preprint).
• Dullin, H.R., J.D. Meiss, and J. Worthington, "Poisson Structure of the Three-Dimensional Euler Equations in Fourier Space." J. Phys. A 52(36), 365501 (2019). (arXiv Preprint).

Hamiltonian Dynamics

• J.D. Meiss, "Transport Near the Onset of Chaos", Physics Today, Physics News of 1986, January (1987).
• R.S. MacKay and J.D. Meiss, "The Relation between Quantum and Classical Thresholds for Multi-photon Ionization of Excited Atoms", Phys. Rev. A 37 4702-4706 (1988).
• J.D. Meiss, "Comment on Microwave Ionization of H-atoms: breakdown of classical dynamics for high frequencies", Phys. Rev. Lett. 62 1576 (1989).
• E. Bollt and J.D. Meiss, "Targeting Chaotic Orbits to the Moon", Phys. Lett. A 204 373-378 (1995). (PDF reprint)
• J.E. Howard and J.D. Meiss "Straight Line Orbits in Hamiltonian Flows", Celest. Mech. and Dyn. Astron. 105(4) 337-352 (2009). (arXiv Preprint).
• J.G. Restrepo and J.D. Meiss, "Onset of Synchronization in the Disordered Hamiltonian Mean Field Model", Phys. Rev E, 89 052125 (2014). (arXiv Preprint).
• Y.S. Virkar, J.G. Restrepo and J.D. Meiss, "The Hamiltonian Mean Field model: effect of network structure on synchronization dynamics", Physical Review E 92(5): 052802. (arXiv Preprint).
• Duignan, N. and J.D. Meiss, "Nonexistence of Invariant Tori Transverse to Foliations: An Application of Converse KAM Theory", Chaos 31 013124 (2021). (arXiv Preprint)
• Duignan, N. and J.D. Meiss "Distinguishing between Regular and Chaotic orbits of Flows by the Weighted Birkhoff Average", Physica D 449, 133749 2023 (arXiv Preprint)
• J.D. Meiss "Hamiltonian Triplet Interactions: Areal and Perimetric Forces", SIAM J. Appl. Dyn. Sys.25(2): 1042–1069 (2026) (arXiv Preprint)

Plasma Physics

• Meiss, J.D. and C. W. Horton, "Drift-Wave Turbulence from a Soliton Gas." Phys. Rev. Lett 48: 1362-1364 (1982).
• Meiss, J.D. and C. W. Horton, "Fluctuation Spectra of a Drift Wave Soliton Gas." Phys. Fluids 25: 1838-1843 (1982).
• Meiss, J.D. and C. W. Horton (1983). "Solitary Drift Waves in the Presence of Magnetic Shear." Phys. Fluids 26(4): 990-997 (1983).
• Meiss, J.D. and P. J. Morrison, "Nonlinear Electron Landau Damping of Ion Acoustic Solitons." Phys. Fluids 26: 983-989 (1983).
• Horton, W., J. Liu, J.D. Meiss and J. E. Sedlak, "Solitary Vortices in a Rotating Plasma." Phys. Fluids 29(4): 1004-1010 (1986).
• Mirnov, V.V., J.D. Meiss and J. L. Tennyson (1986). "Relaxation to the Steady State in Neutral-Beam Injected Mirrors", Phys. Fluids 29: 3740-3748 (1986).
• Aydemir, A., R.D. Hazeltine, J.D. Meiss, and M. Kotschenreuther, "Destabilization of Alfven-Resonant Modes by Resistivity and Diamagnetic Drifts", Physics of Fluids 30 4-6 (1987).
• Meiss, J.D., "Transport Near the Onset of Chaos", Physics Today, Physics News of 1986, January (1987).
• Aydemir, A. Y., R.D. Hazeltine, M. Kotschenreuther, J.D. Meiss, P.J. Morrison, D.W Ross, F. L. Waelbroeck, J.C. Wiley, "Nonlinear MHD Studies in Toroidal Geometry", Plasma Physics and Controlled Nuclear Fusion Research 1988, Lausanne, Switzerland (International Atomic Energy Agency, Vienna, 1989), 131-143.
• Meiss, J.D., "Comment on Microwave Ionization of H-atoms: breakdown of classical dynamics for high frequencies", Phys. Rev. Lett 62 1576 (1989).
• Meiss, J.D. and R.D. Hazeltine, "Canonical Coordinates for Guiding Center Particles", Physics of Fluids, B2 2563-2567 (1990).
• Hayashi, T., T. Sato, H.J. Gardner and J.D. Meiss, "Evolution of Magnetic Islands in a Heliac", Physics of Plasmas 2 752-759 (1994).
• Tennyson, J.L., J.D. Meiss and P.J. Morrison, "Self-Consistent Chaos in the Beam-Plasma Instability", Physica D 71 1-17 (1994). (PDF reprint).
• Burby, J., N. Duignan and J.D. Meiss, "Integrability, Normal Forms, and Magnetic Axis Coordinates", J. Math. Phys. 62(12) 122901 (2021). (arXiv Preprint)
• Duignan, N. and J.D. Meiss, "Normal Forms and Near-Axis Expansions for Beltrami Magnetic Fields", Physics of Plasmas 28: 122501 (2021) (arXiv Preprint)
• Burby, J., N. Duignan and J.D. Meiss, "Minimizing Separatrix Crossings through Isoprominence", Plasma Physics and Controlled Fusion 65(4): 045004.(2023) (arXiv Preprint)

Classes of Dynamical Systems

Area-Preserving Maps

• R. S. MacKay, J.D. Meiss, and I. C. Percival, "Resonances in Area Preserving Maps", Physica D 27 1-20 (1987).
• Q. Chen and J.D. Meiss, "Flux, Resonances and the Devil's Staircase for the Sawtooth Map", Nonlinearity 2 347-356 (1988).
• J.D. Meiss and R.L. Dewar, "Minimizing Flux", Proceedings of the Centre for Mathematical Analysis, Australian National University, Mini-conference on CHAOS & ORDER, 1-3 February 1990, Canberra Australia, Nalini Joshi and Robert L. Dewar (eds.), (World Scientific, Singapore, 1991) pp. 97-103.
• J.D. Meiss, "Phenomenology of Area Preserving Twist Maps", in Nonlinear Dynamics and Chaos, R. L. Dewar and B. I. Henry (eds.), (World Scientific Press, 1992), pp. 15-40.
• J.D. Meiss, "Regular Orbits for the Stadium Billiard", in Quantum Chaos-Quantum Measurement, P. Cvitanovic, I. Percival and A. Wirzga (eds.) (Kluwer Academic, Dordrecht, 1991), NATO ASI Series C Vol 358, pp. 145-166.
• R.L. Dewar and J.D. Meiss, "Flux-Minimizing Curves for Reversible Area-Preserving Maps", Physica D 57 476-506 (1992) (PDF reprint).
• J.D. Meiss, "Cantori for the Stadium Billiard", Chaos 2 267-272 (1992).
• J.D. Meiss, "Regular Orbits for the Stadium Billiard", In Quantum Chaos-Quantum Measurement P. Cvitanovic, I. C. Percival and A. Wirzba. (Dordrecht, Kluwer Academic) 145-166 (1992).
• J.D. Meiss, "Transient Measures for the Standard Map", Physica D 74 254-267 (1994). (PDF reprint).
• H. E. Lomelí and J.D. Meiss "Heteroclinic Orbits and Transport in a Perturbed, Integrable Standard Map". Phys. Lett A 269(5/6) 309-318 (1999). (arXiv Preprint)
• H.R. Dullin, D. Sterling and J.D. Meiss "Self-Rotation Number using the Turning Angle", Physica D 145(1-2) 25-46 (2000).
• J.D. Meiss, "Visual Explorations of Dynamics: the Standard Mapping", Pramana, Indian Academy of Sciences, 70 965-988(2008) (arXiv preprint). (Corrected reprint).
• M. Gidea, J.D. Meiss, I. Ugarcovici, H. Weiss, "Applications of KAM Theory to Population Dynamics", J. Biological Dynamics 5(1) 44-63 (2011).
• A.M. Fox and J. D. Meiss, "Critical Invariant Circles in Asymmetric and Multiharmonic Generalized Standard Maps", Comm. Nonl. Sci. and Num. Simul. 19 1004–1026 (2014) . (arXiv Preprint)
• O. Alus, S. Fishman, and J.D. Meiss, "Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase Space", Phys. Rev. E 90(6) 062923 (2014) . (arXiv Preprint)
• J.D. Meiss, "Thirty Years of Turnstiles and Transport", Chaos 25(9): 097602 (2015) ( arXiv preprint)
• Lerman, L.M. and J.D. Meiss, "Mixed Dynamics in a Parabolic Standard Map", Physica D 315 58-71 (2016). (arXiv preprint).
• Alus, O., S. Fishman, and J.D. Meiss, "Probing the statistics of transport in the Henon Map", European Phys. J. Special Topics, 225(5) 1181-1186 (2016) ( Read-Only Link) (arXiv preprint).
• Mitchell, R.A. and J.D. Meiss, "Designing a Finite-Time Mixer: Optimizing Stirring for Two-Dimensional Maps", SIAM J. Dyn. Sys. 16(3), 1514-1542 (2017). (arXiv Preprint).
• Alus, O., S. Fishman, and J.D. Meiss, "Universal exponent for transport in mixed Hamiltonian dynamics", Phys. Rev. E 96(3) 032204 (2017) (arXiv Preprint ).
• Sander, E. and J.D. Meiss, "Birkhoff Averages and Rotational Invariant Circles for Area-Preserving Maps", Physica D 411 132569 (2020) (arXiv Preprint ).
• Lomelí, H.E. and J.D. Meiss, "Symmetry Reduction and Rotation Numbers for Poncelet maps", submitted to Nonlinearity (2023) (arXiv Preprint ).

Symplectic Maps

• H.T. Kook and J.D. Meiss, "Periodic Orbits for Reversible, Symplectic Mappings", Physica D 35 65-86 (1989).
• H.T. Kook and J.D. Meiss, "Application of Newton's Method to Lagrangian Dynamical Systems", Physica D 36 317-326 (1989).
• R.S. MacKay, J.D. Meiss, and J. Stark, "Converse KAM Theory for Symplectic Twist Maps", Nonlinearity 2 555-570 (1989).
• H.T. Kook and J.D. Meiss, "Diffusion in Symplectic Maps", Phys. Rev. A 41 4143-4150 (1990).
• J.D. Meiss, Symplectic Maps , "Variational Principles, and Transport", Reviews of Modern Physics 64 795-848 (1992)
• E.Bollt and J.D. Meiss, "Breakup of Invariant Tori for the Four Dimensional Semi-Standard Map", Physica D 66 282-297 (1993). (PDF reprint).
• R.W. Easton, J.D. Meiss and S. Carver, "Exit Times and Transport for Symplectic Twist Maps", Chaos 3 153-165 (1993).
• E. Bollt and J.D. Meiss, "Controlling Transport Through Recurrences", Physica D, 81 280-294 (1994).
• MacKay, R. S., J.D. Meiss and J. Stark, "An Approximate Renormalization for the Break-up of Invariant Tori with Three Frequencies", Phys. Lett. A 190 417 (1994). (reprint).
• J.D. Meiss, "Towards an Understanding of the Break-up of Invariant Tori", in Proceedings of the International Conference on Dynamical Systems and Chaos, Y. Aizawa, S. Saito and K. Shiraiwa (eds.), (World Scientific,Singapore), 385-394 (1995). (PDF Preprint)
• J.D. Meiss, "On the Break-up of Invariant Tori with Three Frequencies", In Hamiltonian Systems with Three or More Degrees of Freedom (Ed, Simo, C.) Kluwer, Sagaro, Spain, pp. 494-498 (1999). (PDF Preprint)
• H.R. Dullin and J.D. Meiss, "Stability of Minimal Periodic Orbits", Phys. Lett. A 247 227-234 (1998). (PDF reprint)
• Bäcker, A. and J.D. Meiss, "Moser's Quadratic, Symplectic Map", Reg. Chaotic Dyn. 23(6) 654-664 (2018). (arXiv preprint).
• Bäcker, A. and J.D. Meiss, DSWeb Magazine (2018).
• Bäcker, A. and J.D. Meiss, "The Quadfurcation", "Elliptic Bubbles in Moser's 4D Quadratic Map: the Quadfurcation", SIAM J. Dyn. Sys., 19(1) 442-479 (2020), (arXiv preprint).

Three-dimensional Maps

• Meiss, J.D., "Average Exit Times in Volume-Preserving Maps", Chaos 7 139-147 (1997). (PDF reprint).
• Lomelí, H.E. and J.D. Meiss, "Quadratic Volume-Preserving Maps", Nonlinearity 11 557-574 (1998). (arXiv preprint) (PDF preprint).
• Lenz, K.E., H.E. Lomelí and J.D. Meiss, "Quadratic Volume Preserving Maps: an Extension of a Result of Moser", Regular and Chaotic Dynamics 3 122-130 (1999). (PDF preprint).
• Lomelí, H.E. and J.D. Meiss, "Heteroclinic Primary Intersections and Codimension one Melnikov Method for Volume-Preserving Maps", Chaos 10(1) 109-121 (2000). (PDF reprint),
• Gomez, A. and J.D. Meiss, "Volume-Preserving Maps with an Invariant", Chaos 12 289-299 (2002). (PDF reprint)
• Lomelí, H.E. and J.D. Meiss, "Heteroclinic intersections between Invariant Circles of Volume-Preserving Maps", Nonlinearity 16 1573-1595 (2003). (arXiv preprint) (PDF preprint)
• Mullowney, P., K. Julian and J.D. Meiss, "Blinking rolls: chaotic advection in a 3D flow with an Invariant", SIAM J. Appl. Dyn. Sys. 4 159-186 (2005). (PDF reprint)
• Wysham, D.B. and J.D. Meiss, "Numerical Computation of the Stable Manifolds of Tori", Chaos 16 023129 (2006). (arXiv Preprint)
• Gonchenko, S.V., J.D. Meiss and I.I. Ovsyannikov, "Chaotic Dynamics of Three-Dimensional Henon Maps That Originate from a Homoclinic Bifurcation", Reg. and Chaotic Dynamics 11 191-212 (2006) (arXiv preprint).
• Meiss, J.D. "Dynamics of Volume-Preserving Maps", Lecture at MSRI, Jan 2007
• Dullin, H.R. and J.D. Meiss, "Nilpotent Normal form for Divergence Free Vector Fields and Volume-Preserving Maps", Physica D 237(2): 156-166 (2008) (arXiv preprint).
• Lomelí, H.E., J.D. Meiss, and R. Ramirez-Ros, "Canonical Melnikov Theory for Diffeomorphisms", Nonlinearity 21 485-508 (2008) (arXiv preprint).
• Mullowney, P., K. Julien, and J.D. Meiss, "Chaotic Advection in the Kuppers-Lortz State", Chaos 18 033104 (2008). (arXiv preprint).
• Lomelí, H.E. and J.D. Meiss, "Generating Forms for Exact Volume-Preserving Maps", Discrete and Continuous Dynamical Systems 2 361-377 (2009) (arXiv preprint).
• Dullin, H.R. and J.D. Meiss, "Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations", SIAM J. Appl. Dyn. Sys. 8 76-128 (2009) (arXiv preprint).
• Lomelí, H.E. and J.D. Meiss, "Resonance Zones and Lobe Volumes for Volume-Preserving Maps", Nonlinearity, 22 1761-1789 (2009) (arXiv preprint).
• Dullin, H.R. and J.D. Meiss, "Resonances and Twist in Volume-Preserving Maps", SIAM J. Appl. Dyn. Sys. 11 319-359 (2012) (arXiv Preprint).
• Meiss, J.D., "The Destruction of Tori in Volume-Preserving Maps", Comm. Nonl. Sci. and Num. Simul. 17 2108-2121, (2012) (arXiv Preprint).
• Dullin, H. R., H. Lomelí and J.D. Meiss, "Symmetry Reduction by Lifting for Maps", Nonlinearity, 25 1709-1733 (2012). (arXiv Preprint).
• Fox, A.M. and J.D. Meiss, "Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps", Physica D 243 45-63 (2013) . (arXiv Preprint).
• Fox, A. M. and J.D. Meiss, "Computing the Conjugacy of Invariant Tori for Volume-Preserving Maps", SIAM J. Appl. Dyn. Sys. 15(1): 557-579 (2016) . (arXiv Preprint).
• Guillery, N. and J.D. Meiss, "Diffusion and Drift in Volume-Preserving Maps", Regular and Chaotic Dynamics, 22(6) 700-720 (2017). (arXiv Preprint).
• Meiss, J.D., N. Miguel, C. Simo, A. Vieiro, "Accelerator modes and anomalous diffusion in 3D volume-preserving maps", Nonlinearity, 31(12) 5615-5642 (2018). (arXiv Preprint)
• Meiss, J.D. and E. Sander, "Birkhoff Averages and the Breakdown of Invariant Tori in Volume-Preserving Maps", Physica D 428 133048 (2021), ( arXiv Preprint)
• Hampton, A.E. and J.D. Meiss, "Anti-Integrability for Three-Dimensional Quadratic Maps", SIAM J. Dyn. Sys., 21(1): 650-675 (2022), ( arXiv Preprint)
• Hampton, A.E. and J.D. Meiss, “The three-dimensional generalized Hénon map: Bifurcations and attractors”, Chaos 32(11): 113127 (2022) (arXiv Preprint)
• Hampton, A.E. and J.D. Meiss, “Connecting Anti-integrability to Attractors for Three-Dimensional, Quadratic Diffeomorphisms” SIAM J. Dyn. Sys. 21(1): 616-640 (2024) (arXiv Preprint)

Phemomena and Methods

Anti-Integrability

• Q. Chen, R.S. MacKay, and J.D. Meiss, "Cantori for Symplectic Maps", J Physics A 23 L1093-L1100 (1990).
• R.S. MacKay and J.D. Meiss, "Cantori for Symplectic Maps near the Anti-integrable Limit", Nonlinearity 5 149-160 (1992).
• D. Sterling and J.D. Meiss, "Computing Periodic Orbits using the Anti-Integrable Limit", Phys. Lett. A 241(1/2) 46-52 (1998). (Preprint)
• D. Sterling, H. R. Dullin and J.D. Meiss, "Homoclinic Bifurcations for the Hénon Map", Physica D 134 153-184 (1999). (Preprint).
• R. W. Easton, J.D. Meiss, G. Roberts, "Drift by Coupling to an Anti-Integrable Limit", Physica D 156 201-218 (2001). (PDF reprint)
• H.R. Dullin, J.D. Meiss, and D. Sterling, "Symbolic Codes for Rotational Orbits", SIAM J.Appl. Dyn. Sys. 4 515-562 (2005). (arXiv Preprint) (PDF reprint)
• J.D. Meiss "Integrability, Anti-Integrability and Volume-Preserving Maps", CMS Notes 14(4) 13-14 (2015)
• Hampton, A.E. and J.D. Meiss "Anti-Integrability for Three-Dimensional Quadratic Maps", SIAM J. Dyn. Sys., 21(1): 650-675, ( arXiv Preprint)
• Hampton, A.E. and J.D. Meiss, “The three-dimensional generalized Hénon map: Bifurcations and attractors”, Chaos 32(11): 113127 (2022) (arXiv Preprint)
• Hampton, A.E. and J.D. Meiss, “Connecting Anti-integrability to Attractors for Three-Dimensional, Quadratic Diffeomorphisms” SIAM J. Dyn. Sys. 21(1): 616-640 (2024) (arXiv Preprint)

Converse KAM Theory

• MacKay, R.S., J.D. Meiss, and J. Stark, "Converse KAM Theory for Symplectic Twist Maps", Nonlinearity 2 555-570 (1989).
• Duignan, N. and J.D. Meiss "Nonexistence of Invariant Tori Transverse to Foliations: An Application of Converse KAM Theory", Chaos 31 013124 (2021). (arXiv Preprint)

Invariant Tori

• E.Bollt and J.D. Meiss, "Breakup of Invariant Tori for the Four Dimensional Semi-Standard Map", Physica D 66 282-297 (1993). (PDF reprint).
• MacKay, R. S., J.D. Meiss and J. Stark, "An Approximate Renormalization for the Break-up of Invariant Tori with Three Frequencies", Phys. Lett. A 190 417 (1994). (PDF reprint).
• J.D. Meiss, "Towards an Understanding of the Break-up of Invariant Tori", in Proceedings of the International Conference on Dynamical Systems and Chaos, Y. Aizawa, S. Saito and K. Shiraiwa (eds.), (World Scientific,Singapore), 385-394 (1995). (PDF Preprint)
• J.D. Meiss, "On the Break-up of Invariant Tori with Three Frequencies", In Hamiltonian Systems with Three or More Degrees of Freedom (Ed, Simo, C.) Kluwer, Sagaro, Spain, pp. 494-498 (1999). (PDF Preprint)
• D.B. Wysham and J.D. Meiss, "Numerical Computation of the Stable Manifolds of Tori", Chaos 16 023129 (2006). (arXiv Preprint)
• H.R. Dullin and J.D. Meiss, "Quadratic Volume-Preserving Maps: Invariant Circles and Bifurcations", SIAM J. Appl. Dyn. Sys. 8 76-128 (2009) (arXiv preprint)
• J.D. Meiss, "The Destruction of Tori in Volume-Preserving Maps", Comm. in Nonl. Sci. and Num. Simul. 17 2108-2121 (2012) (arXiv Preprint)
• A.M. Fox and J. D. Meiss, "Greene's Residue Criterion for the Breakup of Invariant Tori of Volume-Preserving Maps", Physica D 243 45-63 (2013) . (arXiv Preprint)
• A.M. Fox and J. D. Meiss, "Critical Invariant Circles in Asymmetric and Multiharmonic Generalized Standard Maps", Comm. in Nonl. Sci. and Num. Simul. 19(4) 1004–1026 (2014) (arXiv Preprint)
• A.M. Fox and J. D. Meiss, "Efficient Computation of Invariant Tori in Volume-Preserving Maps", submitted to SIAM J. Dyn. Sys. Feb 2014. (arXiv Preprint)
• Sander, E. and J.D. Meiss, "Birkhoff Averages and Rotational Invariant Circles for Area-Preserving Maps", Physica D 411 132569 (2020) (arXiv Preprint ).
• Duignan, N. and J.D. Meiss "Nonexistence of Invariant Tori Transverse to Foliations: An Application of Converse KAM Theory", Chaos 31 013124 (2021). (arXiv Preprint)
• Meiss, J.D. and E. Sander "Birkhoff Averages and the Breakdown of Invariant Tori in Volume-Preserving Maps", Physica D 428(15): 133048 (2021)., ( arXiv Preprint)
• Duignan, N. and J.D. Meiss "Distinguishing between Regular and Chaotic orbits of Flows by the Weighted Birkhoff Average", Physica D 449, 133749 (2023) (arXiv Preprint)

Piecewise Smooth Bifurcations

• D.J.W. Simpson and J.D. Meiss, "Andronov-Hopf Bifurcations in Planar, Piecewise-Smooth, Continuous Flows", Phys. Lett. A 371(3) 213-220 (2007) (arXiv preprint).
• D.J.W. Simpson and J.D. Meiss, "Neimark-Sacker Bifurcations in Planar, Piecewise Smooth, Continuous Maps", SIAM J. Appl. Dyn. Sys. 7(3) 795-824 (2008)
• D.J.W. Simpson and J.D. Meiss, "Unfolding a Codimension-Two, Discontinuous, Andronov-Hopf Bifurcation", Chaos 18 033125 (2008) (arXiv preprint)
• D.J.W. Simpson, D.S. Kompala, and J.D. Meiss, "Discontinuity Induced Bifurcations in a Model of Saccharomyces cerevisiae", Math. Biosciences 218 40-49(2009) (arXiv preprint) (PDF reprint)
• D.J.W. Simpson and J.D. Meiss, "Shrinking Point Bifurcations of Resonance Tongues for Piecewise-Smooth, Continuous Maps", Nonlinearity 22 1123-1144 (2009) (arXiv preprint)
• D.J.W. Simpson and J.D. Meiss, "Simultaneous Border-Collision and Period-Doubling Bifurcations", Chaos 19 033146 (2009) (arXiv preprint)
• D.J.W. Simpson and J.D. Meiss, "Resonance near Border-Collision Bifurcations in Piecewise-Smooth, Continuous Maps", Nonlinearity 23 3091-3118 (2010) (arXiv preprint)
• D.J.W. Simpson and J.D. Meiss, "Aspects of Bifurcation Theory for Piecewise-Smooth, Continuous Systems", Physica D 241(22) 1861-1868 (2012) (arXiv preprint)

Polynomial Maps

• H.R. Dullin and J.D. Meiss, "Generalized Hénon Maps: the Cubic Polynomial Diffeomorphisms of the Plane", Physica D 143(1-4) 262-289 (2000) .
• A. Gómez and J.D.Meiss, "Reversible Polynomial Automorphisms of the Plane: the Involutory Case", Phys. Lett. A 312 49-58 (2003). (PDF reprint)
• A. Gómez and J.D. Meiss, "Reversible Polynomial Automorphisms in the Plane", Nonlinearity 17 975-1000 (2003). (arXiv preprint) (PDF reprint)
• Gonchenko, S.V., J.D. Meiss and I.I. Ovsyannikov, "Chaotic Dynamics of Three-Dimensional Hénon Maps That Originate from a Homoclinic Bifurcation", Reg. and Chaotic Dynamics 11 191-212 (2006) (arXiv preprint)
• Bäcker, A. and J.D. Meiss, "Moser's Quadratic, Symplectic Map", Reg. Chaotic Dyn. 23(6) 654-664 (2018). (arXiv preprint).
• Bäcker, A. and J.D. Meiss, "The Quadfurcation", DSWeb Magazine (2018).
• Bäcker, A. and J.D. Meiss, Elliptic Bubbles in Moser's 4D Quadratic Map: the Quadfurcation", SIAM J. Dyn. Sys., 19(1) 442-479 (2020), (arXiv preprint). ( arXiv Preprint)
• Hampton, A.E. and J.D. Meiss, "Anti-Integrability for Three-Dimensional Quadratic Maps", SIAM J. Dyn. Sys., 21(1): 650-675, ( arXiv Preprint)
• Hampton, A.E. and J.D. Meiss, “The three-dimensional generalized Hénon map: Bifurcations and attractors”, Chaos 32(11): 113127 (2022) (arXiv Preprint)
• Hampton, A.E. and J.D. Meiss “Connecting Anti-integrability to Attractors for Three-Dimensional, Quadratic Diffeomorphisms” SIAM J. Dyn. Sys. 21(1): 616-640 (2024) (arXiv Preprint)

Semantics and Textual Dynamics

• Doxas, I., J. Meiss, S. Bottone, T. Strelich, A. Plummer, A. Breland, S. Dennis, K. Garvin-Doxas, and M. Klymkowsky "Narrative as a Dynamical System", (arXiv Preprint)
• Doxas, I., J. Meiss, S. Bottone, T. Strelich, A. Plummer, A. Breland, S. Dennis, K. Garvin-Doxas, and M. Klymkowsky "The Dynamical Principles of Storytelling" (arXiv Preprint)

Solitons

• Meiss, J.D. and N. R. Pereira, "Internal Wave Solitons", "Phys. Fluids 21(4): 700-702 (1978).
• Meiss, J.D. and C. W. Horton, "Drift-Wave Turbulence from a Soliton Gas." Phys. Rev. Lett 48: 1362-1364 (1982).
• Meiss, J.D. and C. W. Horton, "Fluctuation Spectra of a Drift Wave Soliton Gas." Phys. Fluids 25: 1838-1843 (1982).
• Meiss, J.D. and C. W. Horton (1983). "Solitary Drift Waves in the Presence of Magnetic Shear." Phys. Fluids 26(4): 990-997 (1983).
• Meiss, J.D. and P. J. Morrison, "Nonlinear Electron Landau Damping of Ion Acoustic Solitons." Phys. Fluids 26: 983-989 (1983).
• Morrison, P. J., J.D. Meiss and J. R. Cary, "Scattering of Regularized-Long-Wave Solitary Waves." Physica D 11(3): 324-336 (1984).
• Horton, W., J. Liu, J.D. Meiss and J. E. Sedlak, "Solitary Vortices in a Rotating Plasma." Phys. Fluids 29(4): 1004-1010 (1986).

Synchronization

• J.G. Restrepo and J.D. Meiss, "Onset of Synchronization in the Disordered Hamiltonian Mean Field Model", Phys. Rev E, 89 052125 (2014). (arXiv Preprint).
• Y.S. Virkar, J.G. Restrepo and J.D. Meiss, "The Hamiltonian Mean Field model: effect of network structure on synchronization dynamics", Physical Review E 92(5): 052802. (arXiv Preprint).

Transitory Dynamics

• Mosovsky, B.A. and J.D. Meiss, "Transport in Transitory Dynamical Systems", SIAM J. Dyn. Syst. 10 35-65 (2011) (arXiv preprint) (PDF reprint).
• Mosovsky, B.A. and J.D. Meiss, "Transport in Transitory, Three-Dimensional, Liouville Flows", SIAM J. Dyn. Sys. 11(4) 1785-1816 (2012) (arXiv preprint) (PDF reprint).
• Mosovsky, B.A., M.F.M. Speetjens, and J.D. Meiss, "Finite-Time Transport in Volume-Preserving Flows", Phys. Rev. Lett 110(21) 214101 (2013)

Transport

• J.D. Meiss, "Transport Near the Onset of Chaos", Physics Today, Physics News of 1986, January (1987).
• J.D. Meiss, Symplectic Maps, Variational Principles, and Transport, Reviews of Modern Physics 64 795-848 (1992) (reprint)
• R.W. Easton, J.D. Meiss and S. Carver, "Exit Times and Transport for Symplectic Twist Maps", Chaos 3 153-165 (1993).
• E. Bollt and J.D. Meiss, "Controlling Transport Through Recurrences", Physica D, 81 280-294 (1994).
• H. E. Lomelí and J.D. Meiss "Heteroclinic Orbits and Transport in a Perturbed, Integrable Standard Map". Phys. Lett A 269(5/6) 309-318 (1999). (arXiv Preprint)
• H. E. Lomelí and J.D. Meiss, "Heteroclinic Primary Intersections and Codimension one Melnikov Method for Volume Preserving Maps", Chaos 10(1) 109-121 (2000). (PDF reprint),
• B.A. Mosovsky and J.D. Meiss, "Transport in Transitory Dynamical Systems", SIAM J. Dyn. Syst. 10 35-65 (2011) (arXiv preprint) (PDF reprint)
• B.A. Mosovsky and J.D. Meiss, "Transport in Transitory, Three-Dimensional, Liouville Flows", SIAM J. Dyn. Sys. 11(4) 1785-1816 (2012) (arXiv preprint) (PDF reprint)
• B.A. Mosovsky, M.F.M. Speetjens, and J.D. Meiss, "Finite-Time Transport in Volume-Preserving Flows", Phys. Rev. Lett 110(21) 214101 (2013)
• O. Alus, S. Fishman, and J.D. Meiss, "Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase Space", Phys. Rev. E 90(6) 062923 (2014) . (arXiv Preprint)
• K.R. Pratt, J.D. Meiss, and J.P. Crimaldi, "Reaction Enhancement of Initially Distant Scalars by Lagrangian Coherent Structures", Phys. Fluids 27 035106 (2015). (Preprint).
• J.D. Meiss, "Thirty Years of Turnstiles and Transport", Chaos 25(9): 097602 (2015) ( arXiv preprint)
• L.M. Lerman and J.D. Meiss, "Mixed Dynamics in a Parabolic Standard Map", Physica D 315 58-71 (2016). ( arXiv preprint)
• Alus, O., S. Fishman, and J.D. Meiss, Universal exponent for transport in mixed Hamiltonian dynamics, Phys. Rev. E 96(3) 032204 (2017) (arXiv Preprint ).
• Guillery, N. and J.D. Meiss, "Diffusion and Drift in Volume-Preserving Maps", Regular and Chaotic Dynamics, 22(6) 700-720 (2017) (arXiv Preprint).
• Meiss, J.D., N. Miguel, C. Simo, A. Vieiro, Accelerator modes and anomalous diffusion in 3D volume-preserving maps", Nonlinearity, 31(12) 5615-5642 (2018). (arXiv Preprint)
• Homan, J.R., and J.D. Meiss, "Noise-enhanced Stickiness in the Harper Map."  Chaos 36(4): 043102. (2026) ( arXiv Preprint)

Twistless Bifurcations

• H. R. Dullin, J.D. Meiss and D. Sterling, "Generic Twistless Bifurcations", Nonlinearity 13 203-224 (2000). (Preprint)
• H.R. Dullin and J.D. Meiss, "Twist Singularities for Symplectic Maps", Chaos 13 1-16 (2003). (PDF reprint)
• H.R. Dullin, A.V. Ivanov and J.D. Meiss, "Normal Forms for 4D Symplectic Maps with Twist Singularities", Phyisca D 215 175-190(2006). (arXiv Preprint)
• H.R. Dullin and J.D. Meiss, "Resonances and Twist in Volume-Preserving Maps", SIAM J. Appl. Dyn. Sys. 11 319-359 (2012) (arXiv Preprint)

Transitory Dynamics

• B.A. Mosovsky and J.D. Meiss, "Transport in Transitory Dynamical Systems", SIAM J. Dyn. Syst. 10 35-65 (2011) (arXiv preprint) (PDF reprint)
• B.A. Mosovsky and J.D. Meiss, "Transport in Transitory, Three-Dimensional, Liouville Flows", SIAM J. Dyn. Sys. 11(4) 1785-1816 (2012) (arXiv preprint) (PDF reprint)
• B.A. Mosovsky, M.F.M. Speetjens, and J.D. Meiss, "Finite-Time Transport in Volume-Preserving Flows", Phys. Rev. Lett 110(21) 214101 (2013)

Transport

• MacKay,R.S.and J.D. Meiss, "Flux and Differences in Action for Continuous Time Hamiltonian Systems." J. Phys. A 19: L225-L229 (1986).
• Meiss, J.D.. "Transport Near the Onset of Stochasticity." J. Part. Accel. 19: 9-24. (1986)
• Meiss, J.D., "Class Renormalization: Islands around Islands", Phys. Rev. A 34: 2375-2383 (1986).
• MacKay, R.S. and Meiss, J.D. and Percival, I.C., "Transport in Hamiltonian Systems", Physica D 13 55-81 (1984).
• Meiss, J.D. and E. Ott, "Markov Tree Model of Transport in Area-Preserving Maps." Physica D 20: 387-402 (1986).
• Meiss, J.D., "Transport Near the Onset of Chaos", Physics Today, Physics News of 1986, January (1987).
• Meiss, J.D., "Symplectic Maps, Variational Principles, and Transport", Reviews of Modern Physics 64 795-848 (1992) (reprint).
• Easton, R.W., J.D. Meiss and S. Carver, "Exit Times and Transport for Symplectic Twist Maps", Chaos 3 153-165 (1993).
• Bollt, E. and J.D. Meiss, "Controlling Transport Through Recurrences", Physica D, 81 280-294 (1994).
• Lomelí, H.E. and J.D. Meiss "Heteroclinic Orbits and Flux in a Perturbed, Integrable Standard Map", Phys. Lett A 269(5/6) 309-318 (1999). (arXiv Preprint)
• Lomelí, H.E. ; and J.D. Meiss, "Heteroclinic Primary Intersections and Codimension one Melnikov Method for Volume-Preserving Maps", Chaos 10(1) 109-121 (2000). (PDF reprint).
• Mosovsky, B.A. and J.D. Meiss, "Transport in Transitory Dynamical Systems", SIAM J. Dyn. Syst. 10 35-65 (2011) (arXiv preprint) (PDF reprint).
• Mosovsky, B.A. and J.D. Meiss, "Transport in Transitory, Three-Dimensional, Liouville Flows", SIAM J. Dyn. Sys. 11(4) 1785-1816 (2012) (arXiv preprint) (PDF reprint).
• Mosovsky, B.A., M.F.M. Speetjens, and J.D. Meiss, "Finite-Time Transport in Volume-Preserving Flows", Phys. Rev. Lett 110(21) 214101 (2013)
• Alus, O., S. Fishman, and J.D. Meiss, "Statistics of the Island-Around-Island Hierarchy in Hamiltonian Phase Space", Phys. Rev. E 90(6) 062923 (2014) . (arXiv Preprint).
• Pratt, K.R., J.D. Meiss, and J.P. Crimaldi, "Reaction Enhancement of Initially Distant Scalars by Lagrangian Coherent Structures", Phys. Fluids 27 035106 (2015). (Preprint).
• Meiss, J.D., "Thirty Years of Turnstiles and Transport", Chaos 25(9): 097602 (2015) (arXiv preprint).
• Lerman, L.M. and J.D. Meiss, "Mixed Dynamics in a Parabolic Standard Map", Physica D 315 58-71 (2016). (arXiv preprint).
• Alus, O., S. Fishman, and J.D. Meiss, "Probing the statistics of transport in the Henon Map", European Phys. J. Special Topics, 225(5) 1181-1186 (2016) (arXiv preprint).
• Mitchell, R.A., and J.D. Meiss, "Designing a Finite-Time Mixer: Optimizing Stirring for Two-Dimensional Maps." SIAM J. Dyn. Sys. 16(3), 1514-1542 (2017). (arXiv Preprint).
• Alus, O., S. Fishman, and J.D. Meiss, Universal exponent for transport in mixed Hamiltonian dynamics, Phys. Rev. E 96(3) 032204 (2017) (arXiv Preprint ).
• Guillery, N. and J.D. Meiss, "Diffusion and Drift in Volume-Preserving Maps", Regular and Chaotic Dynamics, 22(6) 700-720 (2017) (arXiv Preprint).
• Meiss, J.D., N. Miguel, C. Simo, A. Vieiro, Accelerator modes and anomalous diffusion in 3D volume-preserving maps", Nonlinearity, 31(12) 5615-5642 (2018). (arXiv Preprint)
• Homan, J.R., and J.D. Meiss, "Noise-enhanced Stickiness in the Harper Map." Chaos 36(4): 043102. (2026) ( arXiv Preprint)

Weighted Birkhoff Averages

• Sander, E. and J.D. Meiss, "Birkhoff Averages and Rotational Invariant Circles for Area-Preserving Maps", Physica D 411 132569 (2020) (arXiv Preprint ).
• Meiss, J.D. and E. Sander, "Birkhoff Averages and the Breakdown of Invariant Tori in Volume-Preserving Maps", Physica D 428 133048 (2021), ( arXiv Preprint)
• Duignan, N. and J.D. Meiss "Distinguishing between Regular and Chaotic orbits of Flows by the Weighted Birkhoff Average", Physica D 449, 133749 2023 (arXiv Preprint)
• Meiss, J.D. and E. Sander, "Resonance and Weak Chaos in Quasiperiodically-Forced Circle Maps", Comm. Nonl. Sci. and Num. Simul. 142 108562 2025 ( arXiv Preprint)
• Sander, E. and J.D. Meiss, "Proportions of Incommensurate, Resonant, and Chaotic Orbits for Torus Maps", Chaos 35(1): 013147 2025 ( arXiv Preprint)
• Sander, E. and J.D. Meiss, "Computing Lyapunov Exponents using Weighted Birkhoff Averages", J. Phys. A. 38: 355701 2025 (arXiv Preprint)