### An approach for constructing SRB-measures for chaotic attractors

**Pesin, Y ***(Penn State University)*

Thursday 28 November 2013, 10:00-11:00

Seminar Room 2, Newton Institute Gatehouse

#### Abstract

I will discuss a general approach for constructing SRB measures for diffeomorphisms possessing chaotic attractors (i.e., attractors with nonzero Lyapunov exponents). I introduce a certain recurrence condition on the iterates of Lebesgue measure called “effective hyperbolicity” and I will show that if the asymptotic rate of effective hyperbolicity is exponential on a set of positive Lebesgue measure, then the system has an SRB measure. Along the way a new notion of hyperbolicity -- "effective hyperbolicity'' will be introduced and a new example of a chaotic attractor will be presented. This is a joint work with V. Climenhaga and D. Dolgopyat.

#### Video

This talk has not been recorded due to technical difficulties.