The Conley conjecture

• 成果类型: Article
• 署名作者: Ginzburg, Viktor L.
• 刊物名称: ANNALS OF MATHEMATICS
• ISSN/ISSBN: 0003-486X
• 发表日期: 2010
• 页码: 1127-1180
• 关键词: symplectically aspherical manifolds; morse-theory; hamiltonian-dynamics; periodic-orbits; hofers l(infinity)-geometry; lagrangian intersections; CLOSED GEODESICS; FLOER HOMOLOGY; systems; index

摘要

We prove the Conley conjecture for a closed symplectically aspherical symplectic manifold: a Hamiltonian diffeomorphism of 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.