Bessa, MárioTorres, Maria Joana2023-05-292023-05-292019M. Bessa, M. J. Torres, There are no proper topological hyperbolic homoclinic classes for area-preserving maps, Proceedings of the Edinburgh Mathematical Society, 63, 1, 217-228, 2019http://hdl.handle.net/10400.2/13880We begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class Λ associated with an area-preserving homeomorphism f on a surface M is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then Λ = M and f is an Anosov homeomorphism.engShadowingExpansivenessTopological dynamicsHomoclinic classesjournal article10.1017/S0013091519000282