Geometry & Topology, Vol. 7 (2003) Paper no. 20, pages 713--756.

Periodic points of Hamiltonian surface diffeomorphisms

John Franks, Michael Handel

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 S^2 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

AMS subject classification. Primary: 37J10. Secondary: 37E30.

DOI: 10.2140/gt.2003.7.713

E-print: arXiv:math.DS/0303296

Submitted to GT on 28 March 2003. (Revised 26 October 2003.) Paper accepted 29 October 2003. Paper published 30 October 2003.

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John Franks, Michael Handel
Department of Mathematics, Northwestern University
Evanston, IL 60208-2730, USA
and
Department of Mathematics, CUNY, Lehman College
Bronx, NY 10468, USA

Email: john@math.northwestern.edu, handel@g230.lehman.cuny.edu

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