Periodic points of Hamiltonian surface diffeomorphisms
91 citations recorded by the source corpus.
The main result of this paper is that every non-trivial Hamiltonian dieomor- phism of a closed oriented surface of genus at least one has periodic points of arbitrarily high period. The same result is true for S 2 provided the dif- feomorphism has at least three xed points. In addition we show that up to isotopy relative to its xed point set, every orientation preserving dieomor- phism F : S! S of a closed orientable surface has a normal form. If the xed point set is nite this is just the Thurston normal form.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/5a2b55b891d2d8270f7128dea44a36a0cf53ae78
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In Geometry and Topology
- Basak Z. Gurel
- V. Ginzburg
- J. Franks
- M. Handel
- Sheila Sandon
- L. Polterovich
- M. Crainic
- Rui Loja Fernandes
In Mathematical Physics
- V. Ginzburg
- Basak Z. Gurel
- J. Franks
- M. Handel
- Sheila Sandon
- M. Crainic
- Rui Loja Fernandes
- Y. Eliashberg
Citations in the corpus
- Distortion elements in group actions on surfaces (2004, methodology): “The main lemma of this section is a consequence of the results and methods of [10].”
- Periodic Orbits of Twisted Geodesic Flows and The Weinstein-Moser Theorem (2007, background): “However, looking at the question from the perspective of the Conley conjecture (see [ FrHa , Gi9, Hi, SZ]) rather than of the Arnold conjecture, one can expect every low level of K to carry infinitely many periodic orbits (not necessarily short), provided that dim M ≥ 2 and M is symplectically asphe”
- Action and index spectra and periodic orbits in Hamiltonian dynamics (2008, background): “(The case of CP(1) is established in Franks and Handel [18].”