#### 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

and

Department of Mathematics, CUNY,
Lehman College

Bronx, NY 10468, USA

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

GT home page

## Archival Version

**These pages are not updated anymore.
They reflect the state of
.
For the current production of this journal, please refer to
http://msp.warwick.ac.uk/.
**