Salem Numbers and Automorphisms of Complex Surfaces

TL;DR

This paper explores the entropy values of automorphisms on complex surfaces, specifically tori and K3 surfaces, providing characterizations and conditions for positive entropy.

Contribution

It offers a complete characterization of entropy values for automorphisms of complex tori and sufficient conditions for positive entropy on K3 surfaces.

Findings

Characterization of entropy values for complex tori automorphisms

Sufficient conditions for positive entropy on K3 surfaces

Insights into automorphism dynamics on complex surfaces

Abstract

For two-dimensional complex tori, we characterize the set of all values of positive entropy that arise from automorphisms. For K3 surfaces, we give suffcient conditions for a positive value to be the entropy of some automorphism.