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.

Notes on file formats

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


GT home page

EMIS/ELibM Electronic Journals

Outdated Archival Version

These pages are not updated anymore. They reflect the state of 21 Apr 2006. For the current production of this journal, please refer to