2011/11/30 by Peter Albers, Will J. Merry · 1 citation
Mathematics · #math.SG #math.DS
paper · pdf · doi:10.1007/s11784-013-0114-7
published as Journal of Fixed Point Theory and Applications, (2013), 201 - 214 · 13 pages, v2: numerous corrections, results unchanged
arxiv created 2013/02/04 · arxiv updated 2013/08/27
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 [San11b]. In addition we prove that if the Rabinowitz Floer homology of the filling is non-zero 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 contactmorphism 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 doesn't happen. Finally, we prove that a generic contactomorphism on ℝ2n+1 has infinitely many geometrically distinct iterated translated points all of which lie in the interior of its support.