Toward a Smooth Ergodic Theory for Infinite Dimensional Systems
Friday, June 24, 2016 - 10:15am - 11:05am
Focusing on settings that are consistent with semiflows defined by dissipative PDEs, I will discuss some first steps toward building a general dynamical systems theory,largely a theory of chaotic systems, for maps and semiflows in Hilbert and Banach spaces. I will present recent progress, including theorems on Lyapunov exponents, periodic solutions and horseshoes, entropy formula and SRB measures, and a notion of almost every initial condition that is natural to the underlying dynamics. An example of shear-induced chaos will be discussed.