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An approach for constructing SRB-measures for chaotic attractors

Presented by: 
Y Pesin [Penn State University]
Date: 
Thursday 28th November 2013 - 10:00 to 11:00
Venue: 
INI Seminar Room 2
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.
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