Topologically stable homeomorphisms of the circle

Abstract

In this paper, we study topologically stable homeomorphisms of the circle. Our results are the following:Theorem 1. A homeomorphism of the circle is topologically stable if and only if it is topologically conjugate to some Morse-Smale diffeomorphism.Theorem 2. There exists a homeomorphism of the circle which has the pseudo-orbit-tracing-property but is not topologically stable.