Appears in collection : 2024 - T2 - WS2 - Group actions with hyperbolicity and measure rigidity

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.