Geometry & Topology 7 (2003) 713–756

DOI: 10.2140/gt.2003.7.713

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 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.

Keywords

Hamiltonian diffeomorphism, periodic points, geodesic lamination

Mathematical Subject Classification

Primary: 37J10

Secondary: 37E30

References

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Publication

Received: 28 March 2003
Revised: 26 October 2003
Accepted: 29 October 2003
Published: 30 October 2003
Proposed: Benson Farb
Seconded: Leonid Polterovich, Joan Birman

Authors