On the stable dynamical spectrum of complex surfaces

TL;DR

This paper characterizes Salem numbers that can be realized as dynamical degrees of automorphisms on complex surfaces like 2-Tori, K3, or Enriques surfaces, linking algebraic number theory with complex dynamics.

Contribution

It provides a classification of Salem numbers associated with automorphisms on specific complex surfaces, advancing understanding of their dynamical spectra.

Findings

Identifies Salem numbers that are dynamical degrees of surface automorphisms

Establishes conditions for Salem numbers to arise from complex surface automorphisms

Connects algebraic properties of Salem numbers with geometric automorphisms

Abstract

We characterize Salem numbers which have some power arising as dynamical degree of an automorphism on a complex (projective) 2-Torus, K3 or Enriques surface.