We 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.

中文翻译：

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区域保持图没有合适的拓扑双曲同宿类

我们首先为同胚定义一个同宿类。然后我们证明如果一个拓扑同宿类Λ与保面积同胚相关F在一个表面上米是拓扑双曲线的（即具有阴影和扩展性），那么Λ=米和F是 Anosov 同胚。