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Complex/Dynamical Systems Seminar - Hector Lomelí

Event Description:

Hector Lomelí, Department of Mathematics, University of Texas at Austin

ON HAMILTONIAN FLOWS WHOSE ORBITS ARE STRAIGHT LINES
 
 
We say that a Hamiltonian $H$ is affine-integrable if its 
flow is linear in time. Trivial examples are Hamiltonians $H(q; p)$ that do
not depend on the coordinate $q$. By a theorem of Moser, every polynomial
Hamiltonian of degree 3 reduces to such a $q$-independent Hamiltonian
via a linear symplectic change of variables. We show that such a reduction is
impossible, in general, for polynomials of degree 4 or higher. But we give a
condition that implies linear-symplectic conjugacy to another simple class of
Hamiltonians. The condition is shown to hold for all nondegenerate Hamiltonians
that are homogeneous of degree 4.
 
The time-1 maps of affice-integrable flows appear in numerical analysis and physics, 
They are known as jolt-maps and constitute the basic building blocks in the so-called Dragt-Finn
factorization of more general symplectic maps. This factorization has proved to
be  useful in symplectic numerical schemes, including the simulation of Hamiltonian
of flows in plasmas.
 
(Joint work with Hans Koch.)
 
Location Information:
Main Campus - Engineering Office Tower  (View Map)
1111 Engineering DR
Boulder, CO
Room: 226: Applied Math Conference Room
Contact Information:
Name: Ian Cunningham
Phone: 303-492-4668
Email: amassist@colorado.edu