May 27 – 31, 2024
Institut Henri Poincaré
Europe/Paris timezone
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Rigidity of u-Gibbs states in partially hyperbolic dynamics

May 31, 2024, 4:30 PM
Amphithéâtre Hermite / Darboux (Institut Henri Poincaré)

Amphithéâtre Hermite / Darboux

Institut Henri Poincaré

11 rue Pierre et Marie Curie 75005 Paris


Asaf Katz (University of Michigan)


SRB measures, being physical measures, are of prime importance in partially hyperbolic systems. Their existence is an open problem - in general. Nevertheless, a related, more general class of measures - known as u-Gibbs states, were known to exist by a theorem of Pesin-Sinai. I will explain how one can adapt the factorization technique, pioneered by Eskin-Mirzakhani, to the setting of smooth dynamics and prove that for quantitatively non-integrable systems a (generalized) u-Gibbs state must be an SRB measure. If time permits, I will try to describe some of the key ideas and constructions of the Eskin-Mirzakhani technique.

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