Periodic points of Hamiltonian surface diffeomorphisms

Franks, John¹ ; Handel, Michael²

¹ Department of Mathematics, Northwestern University, Evanston, Illinois 60208-2730, USA
² Department of Mathematics, CUNY, Lehman College, Bronx, New York 10468, USA

Geometry & topology, Tome 7 (2003) no. 2, pp. 713-756.

Résumé

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.

Détail

DOI : 10.2140/gt.2003.7.713

Keywords: Hamiltonian diffeomorphism, periodic points, geodesic lamination

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