Title: Is chaotic behavior typical among dynamical systems?
Speaker: Professor Yakov Pesin
Speaker Info: Pennsylvania State University
The hyperbolic theory of dynamical systems provides a mathematical foundation for the paradigm that is widely known as "deterministic chaos" -- the appearance of irregular chaotic motions in purely deterministic dynamical systems. This phenomenon is considered as one of the most fundamental discoveries in the theory of dynamical systems in the second part of the last century. The hyperbolic behavior can be interpreted in various ways and the weakest one is associated with dynamical systems with non-zero Lyapunov exponents.Date: Wednesday, November 2, 2005
I will discuss the still-open problem of whether dynamical systems with non-zero Lyapunov exponents are typical. I will outline some recent results in this direction and relation between this problem and recent advances in the Pugh-Shub stable ergodicity theory.