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Periodic points of
Hamiltonian surface diffeomorphisms
John Franks and Michael Handel |
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Geometry & Topology 7 (2003) 713–756
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arXiv: math.DS/0303296 |
Abstract |
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The main result of this paper is that every non-trivial Hamiltonian diffeomorphism of a closed oriented surface of genus at least one has periodic points of arbitrarily high period. The same result is true for provided the diffeomorphism has at least three fixed points. In addition we show that up to isotopy relative to its fixed point set, every orientation preserving diffeomorphism of a closed orientable surface has a normal form. If the fixed point set is finite this is just the Thurston normal form. |
Keywords
Hamiltonian diffeomorphism, periodic points, geodesic
lamination
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Mathematical Subject Classification 2000
Primary: 37J10
Secondary: 37E30
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References |
Forward citations |
Publication
Received: 28 March 2003
Revised: 26 October 2003
Accepted: 29 October 2003
Published: 30 October 2003
Proposed: Benson Farb
Seconded: Leonid Polterovich, Joan Birman
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Authors |
| John Franks | |
| Department of Mathematics Northwestern University Evanston Illinois 60208-2730 USA |
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| Michael Handel | |
| Department of Mathematics CUNY, Lehman College Bronx New York 10468 USA |
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