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expansiveness

Proceedings of the Edinburgh Mathematical Society (1)

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There are no proper topological hyperbolic homoclinic classes for area-preserving maps
Part of
Mário Bessa, Maria Joana Torres
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 63 / Issue 1 / February 2020

Published online by Cambridge University Press:

12 November 2019, pp. 217-228
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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.