15 nov 2023 -- 11:30
Aula Tricerri, DIMaI, Firenze
Seminario di Geometria del Dini
Abstract.
Hénon maps were introduced by Michel Hénon as a simplified model of the Poincaré section of the Lorenz model. They are among the most studied discrete-time dynamical systems that exhibit chaotic behaviour. Complex Hénon maps have been extensively studied over the last three decades, in parallel with the development of pluripotential theory. I will present a recent result obtained with Tien-Cuong Dinh, where we show that the measure of maximal entropy of every complex Hénon map is exponentially mixing of all orders for Hölder observables. As a consequence, the Central Limit Theorem holds for all Hölder observables. A similar property holds for every automorphism of a compact Kähler manifold with simple action on cohomology.