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https://hdl.handle.net/1822/64189| Title: | There are no proper topological hyperbolic homoclinic classes for area-preserving maps |
| Author(s): | Bessa, Mário Torres, M. J. |
| Keywords: | Shadowing Expansiveness Topological dynamics Homoclinic classes |
| Issue date: | 2020 |
| Publisher: | Cambridge University Press |
| Journal: | Proceedings of the Edinburgh Mathematical Society |
| Abstract(s): | We begin by defining a homoclinic class for homeomorphisms. Then we prove that if a topological homoclinic class \Lambda associated to an area-preserving homeomorphism f on a surface M is topologically hyperbolic (i.e. has the shadowing and expansiveness properties), then \Lambda=M and f is an Anosov homeomorphism. |
| Type: | Article |
| URI: | https://hdl.handle.net/1822/64189 |
| DOI: | 10.1017/S0013091519000282 |
| ISSN: | 0013-0915 |
| e-ISSN: | 1464-3839 |
| Publisher version: | https://www.cambridge.org/core/journals/proceedings-of-the-edinburgh-mathematical-society/article/there-are-no-proper-topological-hyperbolic-homoclinic-classes-for-areapreserving-maps/4232BAC3B800704E53605E9CAF044072 |
| Peer-Reviewed: | yes |
| Access: | Open access |
| Appears in Collections: |
Files in This Item:
| File | Description | Size | Format | |
|---|---|---|---|---|
| BessaTorres.pdf | 603,39 kB | Adobe PDF | View/Open |
