A Sufficient Condition for the Existence of Periodic Points of Homeomorphisms on Surfaces

Abstract

Let $\rho_1,\rho_2,\ldots,\rho_{2g+1}$ be rotation vectors for periodic points of a homeomorphism on an orientable surface of genus $g>1$. Assume that the convex hull of the set $\{\rho_1,\rho_2,\ldots,\rho_{2g+1}\}$, Conv$(\rho_1,\rho_2,\ldots,\rho_{2g+1})$, has nonempty interior. We will give a sufficient condition for the existence of a dense subset of Conv$(\rho_1,\rho_2,\ldots,\rho_{2g+1})$ that is realized by periodic points.