The Conley Conjecture

Details The Conley Conjecture The Conley Conjecture

2006-10-31

arxiv.org/abs/math/0610956v2

Mathematics

Symplectic Geometry

46 pages, two figures; minor corrections and typos fixed in the second version

Scientific paper

We prove the Conley conjecture for a closed symplectically aspherical symplectic manifold: a Hamiltonian diffeomorphism of a such a manifold has infinitely many periodic points. More precisely, we show that a Hamiltonian diffeomorphism with finitely many fixed points has simple periodic points of arbitrarily large period. This theorem generalizes, for instance, a recent result of Hingston establishing the Conley conjecture for tori.

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