Exponential mixing of all orders and CLT for generic birational maps of $\mathbb{P}^k$
Dynamical Systems
2024-02-05 v1 Complex Variables
Abstract
For H\'enon maps, Bianchi and Dinh recently proved the exponential mixing of all orders for the measure of maximal entropy and, as a consequence of the recent work of Bj\"orklund and Gorodnik, the CLT for H\"older observables. We extend their results to generic birational maps of . Because of the indeterminacy set, H\"older maps are not stable under iteration, so we need to work with a suitable space of test functions.
Cite
@article{arxiv.2402.01178,
title = {Exponential mixing of all orders and CLT for generic birational maps of $\mathbb{P}^k$},
author = {Henry De Thélin and Gabriel Vigny},
journal= {arXiv preprint arXiv:2402.01178},
year = {2024}
}