DYNAMICAL MODELS FOR SOME TORUS HOMEOMORPHISMS

Abstract. Consider a homeomorphism of the torus T2 in the homotopy class of the identity. There is a topological invariant for f known as the rotation set, which is a compact convex subset of H1(T2,R) ' R2 and describes the homological direction and speed at which the orbits rotate on T2. In this paper we collect some results about the existence of dynamical models associated to this invariant. 1