Title
Transport, flux and growth of homoclinic Floer homology
Author
Faculty/Department
Faculty of Sciences. Mathematics and Computer Science
Publication type
article
Publication
Subject
Mathematics
Source (journal)
Discrete and continuous dynamical systems
Volume/pages
32(2012) :10 , p. 3587-3620
ISSN
1078-0947
ISI
000307644500012
Carrier
E
Target language
English (eng)
Full text (Publishers DOI)
Abstract
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.
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