Every Weak Perron Number is an End-Periodic Stretch Factor

Abstract

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

35 pages, 15 figures