MAT 622E - Chaos&Dynamical Systems

Course Objectives

1. To teach some of the high-level topics of Chaos and Dynamical Systems,
2. To form the necessary background for the graduate students who wish to do research on Chaos and Dynamical Systems.

Course Description

Examples and Basic Concepts: Expanding Endomorphisms of a Circle, The Gauss Transformation, Flows and Differential Equations, Lyapunov Exponents.
Topological Dynamics: Topological Entropy, Applications to Ramsey Theory.
Symbolic Dynamics: Codes, The Perron-Frobenius Theorem, Sofic Shifts.
Ergodic Theory: Measure Theory, Ergodic Theorems, Weyl’s Theorem.
Hyperbolic Dynamics: Orbits, Anosov Diffeomorphisms, Differentiable Manifolds.
Low Dimensional Dynamics: The Sharkovsky Theorem.
Complex Dynamics: Complex Analysis on the Riemann Sphere, The Julia Set and the Mandelbrot Set.