Mathematics of shear-induced Chaos

Lai-Sang Young, Courant Institute
January 28th, 2010 at 4PM–5PM in 60 Evans Hall [Map]

I will discuss (1) a dynamical phenomenon called shear-induced chaos and (2) how to capture the idea of chaos mathematically. The latter is a general review. I will begin with the work of Smale here at Berkeley some 40 years ago and discuss highlights of subsequent developments. Rigorous results on shear-induced chaos are quite recent. Compared to early models of chaos, this kind is milder and more commonplace, giving rise to low dimensional strange attractors in many naturally occurring dynamical settings. I will use examples to illustrate the underlying geometric mechanism, and present theorems to show that they meet standard mathematical criteria for chaos.