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Translated points and Rabinowitz Floer homology

  • Peter Albers
  • Will J. MerryEmail author
Article

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.

Mathematics Subject Classification

53D40 37J10 58J05 

Keywords

Rabinowitz Floer homology leafwise intersections translated points 

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Copyright information

© Springer Basel 2013

Authors and Affiliations

  1. 1.Mathematisches InstitutWWU MünsterGermany
  2. 2.Departement MathematikETH ZürichSwitzerland

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