Transport, Flux And Growth Of Homoclinic Floer Homology

We point out an interesting relation between transport in Hamiltonian dynamics and Floer homology. We generalize homoclinic Floer homology from R-2 and closed surfaces to two-dimensional cylinders. The relative symplectic action of two homoclinic points is identified with the flux through a turnstile (as defined in MacKay & Meiss & Percival [19]) and Mather's [20] difference in action Delta W. The Floer boundary operator is shown to annihilate turnstiles and we prove that the rank of certain filtered homology groups and the flux grow linearly with the number of iterations of the underlying symplectomorphism.


Published in:
Discrete And Continuous Dynamical Systems, 32, 10, 3587-3620
Year:
2012
Publisher:
Springfield, Amer Inst Mathematical Sciences
ISSN:
1078-0947
Keywords:
Laboratories:




 Record created 2013-02-27, last modified 2018-01-28


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