THERE ARE NO PROPER TOPOLOGICAL HYPERBOLIC HOMOCLINIC CLASSES FOR AREA-PRESERVING MAPS

We begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class Lambda associated with an area-preserving homeomorphism f on a surface M is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then Lambda = M and f is an Anosov homeomorphism.