NDLI: Translated points and Rabinowitz Floer homology

Content Provider	Springer Nature Link
Author	Albers, Peter Merry, Will J.
Copyright Year	2013
Abstract	We prove that if a contact manifold admits an exact filling, then every local contactomorphism isotopic to the identity admits a translated point in the interior of its support, in the sense of Sandon [Internat. J. Math. 23 (2012), 1250042]. In addition, we prove that if the Rabinowitz Floer homology of the filling is nonzero, then every contactomorphism isotopic to the identity admits a translated point, and if the Rabinowitz Floer homology of the filling is infinite dimensional, then every contactomorphism isotopic to the identity has either infinitely many translated points, or a translated point on a closed leaf. Moreover, if the contact manifold has dimension greater than or equal to 3, the latter option generically does not happen. Finally, we prove that a generic compactly supported contactomorphism on $${\mathbb{R}^{2n+1}}$$ has infinitely many geometrically distinct iterated translated points all of which lie in the interior of its support.
Starting Page	201
Ending Page	214
Page Count	14
File Format	PDF
ISSN	16617738
Journal	Journal of Fixed Point Theory and Applications
Volume Number	13
Issue Number	1
e-ISSN	16617746
Language	English
Publisher	Springer Basel
Publisher Date	2013-04-26
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Rabinowitz Floer homology leafwise intersections translated points Floer homology and cohomology, symplectic aspects Symplectic mappings, fixed points Elliptic equations on manifolds, general theory Mathematics Analysis Mathematical Methods in Physics
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Modeling and Simulation

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