- English
- فارسی
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:
- R. Devaney, An Introduction to Chaotic Dynamical Systems, Addison-Wesley, 1989.
- M.W. Hirsch, S. Smale, R. Devaney, Differential Equations, Dynamical Systems and an introduction to Chaos, Elsevior, 2004
- S. Wiggins, Introduction to Applied Nonlinear Dynamical Systems and Chaos, Springer, 2003,
- 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