English

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.

Keywords

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