Exponential mixing property for automorphisms of compact Kähler manifolds

Let $f$ be a holomorphic automorphism of a compact Kähler manifold. Assume that $f$ admits a unique maximal dynamic degree $d_p$ with only one eigenvalue of maximal modulus. Let $\mu$ be its equilibrium measure. In this paper, we prove that $\mu$ is exponentially mixing for all d.s.h. test functions.

Keywords

dynamic degree, equilibrium measure, exponential mixing, superpotential

2010 Mathematics Subject Classification

32Hxx, 37Fxx

Full Text (PDF format)

Received 3 June 2020

Received revised 2 October 2020

Accepted 14 October 2020

Published 4 May 2021