MATH-GA.2650-003 Advanced Topics In Anaylsis: Introduction To Dynamical Systems

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3 points

Course Description

This course introduces the student to the first fundamental ideas of differentiable dynamical systems, focusing on hyperbolic dynamics.  Hyperbolicity in dynamical systems refers to the fast separation of nearby orbits. No prior knowledge of the subject is assumed.  I will begin with otivating examples. The three main topics I plan to cover are (1) local theory (stable/unstable/center manifolds) at fixed points, (2) geometric theory of chaotic systems (horseshoes, homoclinic orbits, attractors); and (3) ergodic theory (ergodicity, mixing, Lyapunov exponents).

Prerequisites

For topics (1) and (2), analysis of several variables is a must, basic knowledge of manifolds helpful; measure theory is assumed for topic (3).

Recent Offerings

TBA

Sample Exams

TBA

Recommended Texts

• Dynamical systems by Brin and Stuck