Reversible flows and Manifolds

About the Course

 

Instructor: J.D. Meiss  
Class: MWF 12:00 ECCR 257
Office Hr: W1-2,Th11-12,F1-2 ECOT 236
Text: Differential Dynamical Systems, Revised Edition
J.D. Meiss

$87 list, (30% off if you are a member of SIAM)


Course Materials

  1. Syllabus
  2. Lecture Schedule and HW
  3. Projects: See the project description.  Topic selection due Feb 26, and a proposal is due March 23. For a discussion thread to help find a group, see the Canvas discussion.
  4. Some Resources in Dynamical Systems

Outline

  • Dynamics and Modelling
  • Linear Systems (Mostly a review)
    • Eigenvalues and Vectors
    • Exponentials of Operators
    • Floquet Theory
    • Stability
  • Existence and Uniqueness
    • Contraction Maps
    • Lipschitz Functions
  • Dynamical Systems
    • Flows, Stability
    • Lyapunov Functions
    • Topological Conjugacy
    • Attractors and Omega Limit Sets
    • Poincare Maps
  • Invariant Manifolds
    • Stable and Center Manifolds
    • Normal Form Theory
  • The Phase Plane
    • Topological Phase Portraits
    • Poincare Bendixson Theory
    • Index Theory
  • Chaotic Dynamics
    • Lyapunov Exponents
    • Hyperbolicity
    • Strange Attractors
    • Homoclinic Bifurcations
  • + at least one addtional topic
    • Bifurcations
    • Perturbation Theory
    • Hamiltonian Systems

Grading

Grades in the course will be based on:

  1. homework sets (assigned roughly bi-weekly during the semester).
  2. class participation (extra points for helping me to make this class a lively one)
  3. projects (written project due at the end of the semester).

Homework Ground rules for the homework sets are as follows. You may use any reference book from the library. You are encouraged to discuss the homework problems with other students in the class, and even to work on the problems together, until you get to the point that you understand how to solve the problem. Each student is required to write up and to submit his/her own homework set. You are not permitted to copy another student's homework, even if you worked on the problems together.

Projects: A list of possible projects  is here. Projects will consist of a 15 minute presentation to the class during the last week of the semester or the final exam period and a written report. Project can involve computation, but need not.

Policies