There are no proper topological hyperbolic homoclinic classes for area-preserving maps

Bessa, Mário; Torres, Maria Joana

http://hdl.handle.net/10400.2/13880

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Authors

Bessa, Mário

Torres, Maria Joana

Abstract(s)

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.

Keywords

Shadowing Expansiveness Topological dynamics Homoclinic classes

URI

http://hdl.handle.net/10400.2/13880

Citation

M. 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, 2019