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arXiv · 0908.3286

On the Generic Existence of Periodic Orbits in Hamiltonian Dynamics

Viktor L. Ginzburg·Basak Z. Gurel
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Abstract

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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Viktor L. Ginzburg, Basak Z. Gurel. 2009-08-23. On the Generic Existence of Periodic Orbits in Hamiltonian Dynamics. https://arxiv.org/abs/0908.3286

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