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Existence of physical measures for surface diffeomorphisms

Date: Tuesday, October 11, 2022 14:00 - 15:00
Speaker: Sylvain Crovisier (Université Paris-Saclay)
Location: Heinzel Seminar Room / Office Bldg West (I21.EG.101)
Series: DynamIST
Host: Kaloshin Group

I will explain a relation between the discontinuities of the Lyapunov exponents and of the entropy, with respect to the invariant measures of smooth diffeomorphisms of surfaces.

Among the consequences, one gets an answer to a conjecture by Viana on surfaces: if the Lyapunov exponents are positive for a set with positive area, there exists an SRB measure.

This is a joint work with J. Buzzi and O. Sarig.

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