On the Generic Existence of Periodic Orbits in Hamiltonian Dynamics

Details On the Generic Existence of Periodic Orbits in Hamiltonian Dynamics On the Generic Existence of Periodic Orbits in Hamiltonian Dynamics

2009-08-23

arxiv.org/abs/0908.3286v1

Mathematics

Symplectic Geometry

14 pages

Scientific paper

We prove several generic existence results for infinitely many periodic orbits of Hamiltonian diffeomorphisms or Reeb flows. For instance, 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 such a symplectomorphism necessarily has infinitely many periodic orbits whenever it has one and all periodic points are non-degenerate.

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