Cornell Math - MATH 507, Spring 2007

MATH 618: Smooth Ergodic Theory (Spring 2007)

Instructor: John Smillie

Meeting Time & Room

This is the second semester course in dynamical systems. This course is an introduction to some topics in ergodic theory and with a focus on some applications connected to polygonal billiards. Topics include the ergodic theorem, unique ergodicity and minimality, applications of ergodic theory to continued fractions and rotations of the circle, interval exchange transformations, polygonal billiards, translation surfaces, pseudo-Anosov diffeomorphisms of surfaces, ergodic theory of the horocycle and geodesic flows for SL(2, R)/SL(2, Z) moduli spaces and flows on moduli spaces as a technique for studying translation surfaces.