Strong Positive Recurrence for diffeomorphisms
报告人： Jérôme Buzzi (CNRS, Paris-Saclay University)
时间：2023-07-19 14:00-16:00
地点：Room 1303, Sciences Building No. 1
Abstract: I will present Strong Positive Recurrence for diffeomorphisms or SPR. This new property, introduced in a joint work with Sylvain Crovisier and Omri Sarig, sits between uniform and nonuniform hyperbolicity. On the one hand, it implies quantitative properties of spectral gap type, in particular exponential mixing for the measures maximizing the entropy. On the other hand, it is sufficiently flexible to include all C^\infty smooth surface diffeomorphisms with positive topological entropy. Indeed, it is equivalent to a stability (or continuity) property of the Lyapunov exponents for measures of large entropy.
