A TRIPLE BOUNDARY LEMMA FOR SURFACE HOMEOMORPHISMS

摘要

Given an orientation-preserving and area-preserving homeomorphism f of the sphere, we prove that every point which is in the common boundary of three pairwise disjoint invariant open topological disks must be a fixed point. As an application, if K is an invariant Wada-type continuum, then f(n)|K is the identity for some n 0. Another application is an elementary proof of the fact that invariant disks for a nonwandering homeomorphism homotopic to the identity in an arbitrary surface are homotopically bounded if the fixed point set is inessential. The main results in this article are selfcontained.