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There are no proper topological hyperbolic homoclinic classes for area-preserving maps
Published online by Cambridge University Press: 12 November 2019
Abstract
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.
MSC classification
- Type
- Research Article
- Information
- Proceedings of the Edinburgh Mathematical Society , Volume 63 , Issue 1 , February 2020 , pp. 217 - 228
- Copyright
- Copyright © Edinburgh Mathematical Society 2019
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