Equidistribution for meromorphic maps with dominant topological degree

TL;DR

This paper proves that for certain meromorphic maps on compact Kaehler manifolds, repelling periodic points become uniformly distributed according to the equilibrium measure, and it characterizes points with non-equidistributed backward orbits.

Contribution

It establishes equidistribution of repelling periodic points for meromorphic maps with dominant topological degree and describes the exceptional set of points.

Findings

Repelling periodic points are equidistributed with respect to the equilibrium measure.

The exceptional set of points with non-equidistributed backward orbits is characterized.

The results apply to meromorphic self-maps with dominant topological degree.

Abstract

Let f be a meromorphic self-map on a compact Kaehler manifold whose topological degree is strictly larger than the other dynamical degrees. We show that repelling periodic points are equidistributed with respect to the equilibrium measure of f. We also describe the exceptional set of points whose backward orbits are not equidistributed.