Salem Numbers and Abelian Surface Automorphisms

TL;DR

This paper classifies two-dimensional complex tori based on automorphisms with positive entropy, detailing the specific entropies and the tori that admit such automorphisms, advancing understanding of their dynamical properties.

Contribution

It provides a complete classification of two-dimensional complex tori with automorphisms of positive entropy, linking entropy values to the structure of the tori.

Findings

Identified all possible positive entropy values for automorphisms.

Described the set of tori admitting automorphisms with each entropy value.

Established a correspondence between entropy and torus structure.

Abstract

We classify two-dimensional complex tori admitting automorphisms with positive entropy in terms of the entropies they exhibit. For each possible positive value of entropy, we describe the set of two-dimensional complex tori admitting automorphisms with that entropy.