Geometria Complessa e Geometria Differenziale
Geometria Complessa e Geometria Differenziale
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Every complex Hénon map satisfies the Central Limit Theorem

Fabrizio Bianchi (CNRS and Laboratoire Paul Painlevé, Lille)

created by daniele on 29 Sep 2023
modified on 07 Nov 2023

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.

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