A lower bound on end-periodic stretch factors

Abstract

Given an end-periodic homeomorphism $f:S\to S$ we give a lower bound on the Handel--Miller stretch factor of $f$ in terms of the core characteristic of $f$, which is a measure of topological complexity for an end-periodic homeomorphism. We also show that the growth rate of this bound is sharp.

7 pages, 4 figures, incorporated referee comments, accepted for publication in Proceedings of the AMS