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ISSN (electronic): 1364-0380
ISSN (print): 1465-3060
Periodic points of Hamiltonian surface diffeomorphisms

John Franks and Michael Handel

Geometry & Topology 7 (2003) 713–756

arXiv: math.DS/0303296

Abstract

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 S2 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 F : S S 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
Mathematical Subject Classification 2000
Primary: 37J10
Secondary: 37E30
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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
Authors
John Franks
Department of Mathematics
Northwestern University
Evanston
Illinois 60208-2730
USA
Michael Handel
Department of Mathematics
CUNY, Lehman College
Bronx
New York 10468
USA