Mathematics Department Colloquium: Cantor invariant subsets of conservative 2-dimensional dynamics

Colloquium | September 13 | 4:10-5 p.m. | 60 Evans Hall

 Marie-Claude Arnaud, University of Avignon

 Department of Mathematics

A lot of problems of classical mechanics lead us to the study of the orientation and area preserving diffeomorphisms of surfaces. Among their invariant sets, the simplest ones are the periodic orbits, but more curious invariant sets often exist : Cantor subsets. We will introduce the setting and explain why such invariant Cantor sets often exist. We will focus on two kinds of them: the horseshoes and Denjoy sets and explain that in some sense, they are linked but different.

 vivek@math.berkeley.edu