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A Dichotomy in Area-Preserving Reversible Maps
| Content Provider | Semantic Scholar |
|---|---|
| Author | Bessa, Mário Rodrigues, Alexandre |
| Copyright Year | 2014 |
| Abstract | In this paper we study R-reversible area-preserving maps $$f:M\rightarrow M$$f:M→M on a two-dimensional Riemannian closed manifold M, i.e. diffeomorphisms f such that $$R\circ f=f^{-1}\circ R$$R∘f=f-1∘R where $$R:M\rightarrow M$$R:M→M is an isometric involution. We obtain a $$C^1$$C1-residual subset where any map inside it is Anosov or else has a dense set of elliptic periodic orbits, thus establishing the stability conjecture in this setting. Along the paper we derive the $$C^1$$C1-Closing Lemma for reversible maps and other perturbation toolboxes. |
| Starting Page | 309 |
| Ending Page | 326 |
| Page Count | 18 |
| File Format | PDF HTM / HTML |
| DOI | 10.1007/s12346-015-0155-y |
| Volume Number | 15 |
| Alternate Webpage(s) | https://arxiv.org/pdf/1403.3572v1.pdf |
| Alternate Webpage(s) | https://doi.org/10.1007/s12346-015-0155-y |
| Language | English |
| Access Restriction | Open |
| Content Type | Text |
| Resource Type | Article |
