APPM 7100 Fall 2015

Dynamical Systems

 
 

Topics

  1. One Dimensional Dynamics

  2. Monotone Maps

  3. Circle Maps & Arnold Tongues

  4. Linearization and Stability

  5. Fixed Points and Periodic Orbits

  6. Sinks and Hyperbolic Points

  7. Linear Maps & Contractions

  8. Bifurcations and Normal Forms

  9. Period Doubling Cascades

  10. Renormalization

  11. Versal Unfoldings

  12. Saddle-Node, Pitchfork & Hopf Bifurcations

 
  1.     Lectures

  2.     Syllabus

  3.     Resources

  1. Symplectic Maps

  2. Action & Variational Principals

  3. Twist Maps and Aubry-Mather Theory

  4. Invariant Circles and Cantori

  5. Diffusion and Transport

  6. Hyperbolic Sets and Chaos

  7. Anosov Maps and Cat Maps

  8. Transitivity, Mixing, Ergodicity,

  9. Entropy, Lyapunov exponents

  10. Symbolic Dynamics

  11. Orbit Growth, Mixing

  12. Smale's Horseshoe

  13. Fractals and Scaling

Class:                MWF 12-1   ECCR 257

Instructor:          J.D. Meiss    ECOT 236

Prerequisites:    APPM 5460 or equivalent course

                           in differential equations.

Text:                 My Lecture notes will be posted here

Alternative:       Dynamical Systems, C. Robinson

                         (CRC 1999)