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An approach for constructing SRB-measures for chaotic attractors

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If you have a question about this talk, please contact Mustapha Amrani.

Mathematics for the Fluid Earth

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.

This talk is part of the Isaac Newton Institute Seminar Series series.

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