Geometry & Topology

Periodic points of Hamiltonian surface diffeomorphisms

John Franks and Michael Handel

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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:SS 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

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

Received: 28 March 2003
Revised: 26 October 2003
Accepted: 29 October 2003
First available in Project Euclid: 21 December 2017

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Hamiltonian diffeomorphism periodic points geodesic lamination


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.

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