## Geometry & Topology

### Periodic points of Hamiltonian surface diffeomorphisms

#### 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.

#### Article information

Source
Geom. Topol., Volume 7, Number 2 (2003), 713-756.

Dates
Revised: 26 October 2003
Accepted: 29 October 2003
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513883320

Digital Object Identifier
doi:10.2140/gt.2003.7.713

Mathematical Reviews number (MathSciNet)
MR2026545

Zentralblatt MATH identifier
1034.37028

Subjects
Primary: 37J10: Symplectic mappings, fixed points
Secondary: 37E30: Homeomorphisms and diffeomorphisms of planes and surfaces

#### Citation

Franks, John; Handel, Michael. Periodic points of Hamiltonian surface diffeomorphisms. Geom. Topol. 7 (2003), no. 2, 713--756. doi:10.2140/gt.2003.7.713. https://projecteuclid.org/euclid.gt/1513883320

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