Salem numbers and Enriques surfaces

TL;DR

This paper investigates the relationship between Salem numbers and automorphisms of Enriques surfaces, providing experimental evidence that supports the semi-continuity of dynamical degrees in algebraic families.

Contribution

It explores the realization of small Salem numbers as dynamical degrees of automorphisms on Enriques surfaces, combining theoretical insights with experimental validation.

Findings

Confirmed semi-continuity of dynamical degrees in algebraic families.

Provided experimental evidence for realizing small Salem numbers on Enriques surfaces.

Supported the connection between Salem numbers and surface automorphisms.

Abstract

It is known that the dynamical degree, or equivalently, the topological entropy of an automorphism g of an algebraic surface S is lower semi-continuous when (S,g) varies in a algebraic family. In this paper we make a series of experiments confirming this behavior with the aim to realize small Salem numbers as the dynamical degrees of automorphisms of Enriques surfaces.