Classifying Hyperbolic Ergodic Stationary Measures on Compact Complex Surfaces with Large Automorphism Groups

TL;DR

This paper classifies hyperbolic, ergodic stationary measures on compact complex surfaces with large automorphism groups, expanding understanding of their structure without assuming the presence of parabolic elements.

Contribution

It provides a classification of hyperbolic, ergodic stationary measures on complex surfaces with large automorphism groups, without requiring parabolic elements in the group.

Findings

Classification of hyperbolic, ergodic stationary measures

Analysis of automorphism groups on complex surfaces

Results applicable to non-elementary groups

Abstract

Let $X$ be a compact complex surface. Consider a finitely supported probability measure $\mu$ on $\text{Aut}(X)$ such that $\Gamma_{\mu} = \langle \text{Supp}(\mu)\rangle<\text{Aut}(X)$ is non-elementary. We do not assume that $\Gamma_{\mu}$ contains any parabolic elements. In this paper, we study and classify hyperbolic, ergodic $\mu$-stationary probability measures.