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Discrete Dynamical Systems

  • Examples Of Dynamical Systems, Elementary Definitions, Hyperbolicity, The quadratic Family, Symbolic dynamics, Topological Conjugacy, Chaos, Structural Stability, Sharkovskii's Theorem, Bifurcation Theory.
  • Higher Dimentional Dynamics, Dynamics of linear maps, The horseshoe map, Shift map and Symbolics Dynamics, Attractors, Hyperbolic Sets
  • The Stable, Unstable and Center Manifolds
  • Neimark-Sacker bifurcations, Homoclinic Bifurcations, Poincare map.
  • Homoclinic Phenomena, Lorenz Attractors and Shelnikov Systems

References:

  1. R. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, 1989.
  2. M.W. Hirsch, S. Smale, R. Devaney, Differential Equations, Dynamical Systems and an introduction to Chaos, Elsevior, 2004
  3. S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, 2003,
  4. J. Hale, H. Kocak, Dynamics and Bifurcations, Springer- Verlag, 1991.
Prerequisites: 
  • Analysis1, Linear Algebra
Grading Policy: 
  • Midterm 40%
  • Final 60%
Time: 

Class Hour: Saturday-Monday, 8:00-10:00 Am.

Office hour: Sunday-Tuesday, 11:00-12:00 Am or by appointment

Term: 
Fall 2015
Grade: 
Graduate

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