Cornell Math - MATH 617, Fall 2005

MATH 617: Dynamical Systems (Fall 2005)

Instructor: John Smillie

Meeting Time & Room

This course will be an introduction to Dynamical Systems. We will use the recently published book, "Introduction to Dynamical Systems" by Brin and Stuck. This is a nice book for two reasons. It gives a variety of viewpoints on the field and it has some very nice problems which will be assigned as homework.

Topics will include:

• Topological dynamics and topological entropy.
• Symbolic dynamics, subshifts of finite type and substitution systems.
• Basic hyperbolic theory and applications to celestial mechanics, expanding maps and complex dynamics.
• Continued fractions viewed as a concrete example of renormalization.
• Equidistribution of orbits and applications to polygonal billiards