ON THE GENERIC EXISTENCE OF PERIODIC ORBITS IN HAMILTONIAN DYNAMICS

被引：19

作者：

Ginzburg, Viktor L. ^{[1
]}

Gurel, Basak Z. ^{[2
]}

机构：

[1] Univ Calif Santa Cruz, Dept Math, Santa Cruz, CA 95064 USA

[2] Vanderbilt Univ, Dept Math, Nashville, TN 37240 USA

来源：

JOURNAL OF MODERN DYNAMICS | 2009年 / 3卷 / 04期

关键词：

Periodic orbits; Hamiltonian flows; Floer homology; Conley conjecture; EQUIVARIANT MORSE-THEORY; CLOSED GEODESICS; SUBHARMONIC SOLUTIONS; ENERGY SURFACES; FLOER HOMOLOGY; SYSTEMS; FLOWS; TORI; DIFFEOMORPHISMS; EQUATIONS;

D O I：

10.3934/jmd.2009.3.595

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove several generic existence results for infinitely many periodic orbits of Hamiltonian diffeomorphisms or Reeb flows. For example, we show that a Hamiltonian diffeomorphism of a complex projective space or Grassmannian generically has infinitely many periodic orbits. We also consider symplectomorphisms of the two-torus with irrational flux. We show that a symplectomorphism necessarily has infinitely many periodic orbits if it has one and all periodic points are nondegenerate.

引用

页码：595 / 610

页数：16

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