Strong Positive Recurrence (or SPR) is a new property of diffeomorphisms that sits between uniform and nonuniform hyperbolicity. It can be characterized in terms of Lyapunov exponents and one can show that it is satisfied by all $C^\infty$ diffeomorphisms with positive entropy.

SPR implies that ergodic measures maximizing the Kolmogorov-Sinai entropy are “strongly chaotic” (similar to uniformly hyperbolic in the sense of Anosov and Smale): they exhibit exponential mixing, large deviations, central limit theorem, etc.

Joint work with Sylvain CROVISIER and Omri SARIG.

报告人简介：Jérôme Buzzi 主要研究动力系统, 特别是光滑动力系统的遍历理论. 他是法国国家科学研究中心（CNRS）的高级研究员, 目前在奥赛工作, 此前曾在第戎, 马赛和巴黎综合理工学院任职. 他曾就读于巴黎高等师范学院, 并于1995 年在巴黎第十一大学（现巴黎萨克雷大学）获得博士学位. 在Ann. of Math., Invent. Math. 等高水平期刊发表论文五十多篇.