MATH-GA.2650-003 Advanced Topics In Anaylsis: Introduction To Dynamical Systems
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).
For topics (1) and (2), analysis of several variables is a must, basic knowledge of manifolds helpful; measure theory is assumed for topic (3).
- Dynamical systems by Brin and Stuck