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Periodic points of Hamiltonian surface diffeomorphisms

John Franks·Michael Handel
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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.

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John Franks, Michael Handel. 2003-11-14. Periodic points of Hamiltonian surface diffeomorphisms. https://doi.org/10.2140/gt.2003.7.713

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