Exponential mixing of all orders and CLT for automorphisms of compact Kähler manifolds

Fabrizio Bianchi (1, 2) , Tien-Cuong Dinh (3)

1 CNRS - Centre National de la Recherche Scientifique
2 LPP - Laboratoire Paul Painlevé - UMR 8524
3 NUS - National University of Singapore

We consider the unique measure of maximal entropy of an automorphism of a compact Kähler manifold with simple action on cohomology. We show that it is exponentially mixing of all orders with respect to Hölder observables. It follows that the Central Limit Theorem (CLT) holds for these observables. In particular, our result applies to all automorphisms of compact Kähler surfaces with positive entropy.

Mots clés: Automorphism; Exponential Mixing of all orders; Central Limit Theorem

Domaines: Systèmes dynamiques [math.DS]; Variables complexes [math.CV]

Fabrizio Bianchi, Tien-Cuong Dinh. Exponential mixing of all orders and CLT for automorphisms of compact Kähler manifolds. 2023. ⟨hal-04081236⟩