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On the generic existence of periodic orbits in Hamiltonian dynamics

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  • 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.
    Mathematics Subject Classification: Primary: 53D40; Secondary: 37J10.

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