Migration of wandering points of a surface homeomorphism

We deal with a homeomorphism h of a compact connected locally connected met ric space, with exactly two fixed points, and such that all other points ar e wandering. We prove that there exists a point whose orbit under h goes fr om one fixed point to the other. In case the manifold is the two-dimensiona l sphere, we explain how one can use the index theorem of P. Le Calvez and J.-C. Yoccoz to tell which kinds of orbits such a homeomorphism can have. ( C) 2000 Academie des sciences/Editions scientifiques et medicales Elsevier SAS.