Volume 7, issue 2 (2003)

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Periodic points of Hamiltonian surface diffeomorphisms

John Franks and Michael Handel

Geometry & Topology 7 (2003) 713–756
 arXiv: math.DS/0303296
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 $F:S\to S$ 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
Primary: 37J10
Secondary: 37E30