Every Weak Perron Number is an End-Periodic Stretch Factor

TL;DR

This paper proves that every weak Perron number can be realized as a stretch factor of an end-periodic homeomorphism on a specific class of infinite-type surfaces, expanding the understanding of stretch factors in surface dynamics.

Contribution

It constructs end-periodic homeomorphisms with prescribed weak Perron numbers as their stretch factors on infinite-type surfaces, demonstrating a broad realization result.

Findings

Every weak Perron number is realizable as an end-periodic stretch factor.

Constructs explicit examples of end-periodic homeomorphisms with given stretch factors.

Extends the class of stretch factors known for infinite-type surfaces.

Abstract

Given any weak Perron number $\lambda$, we construct an end-periodic homeomorphism $f:\Sigma\rightarrow \Sigma$ with Handel-Miller stretch factor equal to $\lambda$ where $\Sigma$ is a connected infinite-type surface with finitely many ends all accumulated by genus.