Dynamic Systems Seminars——Existence of Gibbs u-states in C^1 scenario via entropy formula
主 题: Dynamic Systems Seminars——Existence of Gibbs u-states in C^1 scenario via entropy formula
报告人: Dr. Jinhua Zhang (Université Paris-Sud)
时 间: 2018-06-14 09:00-11:00
地 点: Room 1418, Sciences Building No. 1
Abstract: We consider a partially hyperbolic attracting set $\Lambda$ with the splitting of the form $T_\Lambda M=E^{cs}\oplus E^{uu}$ for a $C^1$ diffeomorphism f. We will show that for Leb. a.e. x in the attracting neighborhood of Λ, each empirical measure $\mu$ of x satisfies the partial entropy formula $$h_{\mu}(f,\mathcal{F}^{uu})=\int\log|det(Df|_{E^{uu}})|d\mu.$$ In $C^{1+\alpha}$-scenario, measures satisfy such entropy formula are Gibbs u-states, and our results give some consequences on SRB measures. If time allows, we will also talk about the large deviation property for continuous functions. This is a joint work with Sylvain Crovisier and Dawei Yang.
