Quantitative Dynamics of complex Hénon maps

Abstract

Let $f$ be a Hénon map of ${\mathbb{C}}^2$. We provide quantitative versions of several results involving dynamical objects associated to $f$. Our results can be interpreted as a quantitative version of Pesin theory with geometric control. As an application we show that the perdiodic points of period $n$ of $f$ equidistribute towards its equilibrium measure exponentially fast as $n$ tends to infinity.

First draft. No AI was used in this work