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.

About the reporter: Jérôme Buzzi mainly studies the traversal theory of dynamical systems, especially smooth dynamical systems He is a senior researcher at the French National Centre for Scientific Research (CNRS) and currently works at Osay. He has previously held positions at Dijon, Marseille, and É cole Polytechnique in Paris He studied at the É cole Normale Sup é rieure in Paris and obtained his doctoral degree from the University of Paris XI (now the University of Paris Saclay) in 1995 Published over 50 papers in high-level journals such as Ann. of Math. and Invent. Math.