# Non-contractible Periodic Orbits in Hamiltonian Dynamics on Closed Symplectic Manifolds

```@article{Ginzburg2015NoncontractiblePO,
title={Non-contractible Periodic Orbits in Hamiltonian Dynamics on Closed Symplectic Manifolds},
author={V. Ginzburg and Basak Z. Gurel},
journal={arXiv: Symplectic Geometry},
year={2015}
}```
• Published 2015
• Mathematics
• arXiv: Symplectic Geometry
• We study Hamiltonian diffeomorphisms of closed symplectic manifolds with non-contractible periodic orbits. In a variety of settings, we show that the presence of one non-contractible periodic orbit of a Hamiltonian diffeomorphism of a closed toroidally monotone or toroidally negative monotone symplectic manifold implies the existence of infinitely many non-contractible periodic orbits in a specific collection of free homotopy classes. The main new ingredient in the proofs of these results is a… CONTINUE READING
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