Cornell Math - MATH 617, Fall 2004

MATH 617: Introduction to Dynamical Systems (Fall 2004)

Instructor: John Smillie

Meeting Time & Room

MATH 617 is a mathematically rigorous introduction to some basic techniques in dynamical systems and ergodic theory.

Topics include:

  • Chain recurrence and Lyapunov functions
  • Uniform distribution on the circle and in higher dimensions
  • Interval exchange transformations
  • Expanding maps and structural stability
  • The ergodic theorem
  • Ergodicity of hyperbolic torus maps
  • Geodesic flows on surfaces of negative curvature
  • The horocycle flow
  • Lyapunov exponents and stable manifolds
  • Hyperbolicity