The Conley Conjecture
Symplectic Geometry
2009-06-23 v2 Differential Geometry
Dynamical Systems
Abstract
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.
Cite
@article{arxiv.math/0610956,
title = {The Conley Conjecture},
author = {Viktor L. Ginzburg},
journal= {arXiv preprint arXiv:math/0610956},
year = {2009}
}
Comments
46 pages, two figures; minor corrections and typos fixed in the second version