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Non-contractible periodic orbits in Hamiltonian dynamics on closed symplectic manifolds

Published online by Cambridge University Press:  17 June 2016

Viktor L. Ginzburg
Affiliation:
Department of Mathematics, UC Santa Cruz, Santa Cruz, CA 95064, USA email [email protected]
Başak Z. Gürel
Affiliation:
Department of Mathematics, University of Central Florida, Orlando, FL 32816, USA email [email protected]
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Abstract

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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 filtration of Floer homology by the so-called augmented action. This action is independent of capping and, under favorable conditions, the augmented action filtration for toroidally (negative) monotone manifolds can play the same role as the ordinary action filtration for atoroidal manifolds.

Type
Research Article
Copyright
© The Authors 2016 

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