Exponential decay of correlations for generic birational maps of P^k

TL;DR

This paper proves that generic birational maps of projective space exhibit exponential decay of correlations for certain observables, with improved estimates for regular maps aligning with known results for Hénon maps.

Contribution

It establishes exponential decay of correlations for generic birational maps of P^k and provides sharper decay rate estimates for regular maps, extending Bedford-Diller and Dinh's work.

Findings

Exponential decay of correlations proven for generic birational maps.

Sharper decay rate estimates for regular birational maps.

Results align with known decay rates for Hénon maps.

Abstract

We prove the exponential decay of correlations for C^\alpha-observables (0<\alpha =<2) for generic birational maps of P^k \`a la Bedford-Diller. In the particular case of regular birational maps, we give a better estimate of the speed of the decay, getting results as sharp as Dinh's results for H\'enon maps.