Leaf-wise intersections and Rabinowitz Floer homology

Abstract

In this article we explain how critical points of a particular perturbation of the Rabinowitz action functional give rise to leaf-wise intersection points in hypersurfaces of restricted contact type. This is used to derive existence and multiplicity results for leaf-wise intersection points in hypersurfaces of restricted contact type in general exact symplectic manifolds. The notion of leaf-wise intersection points was introduced by Moser.

18 pages, 1 figure; v3: completely rewritten, improved results

Cited by in corpus (19)

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• Rabinowitz Floer homology: A survey
• A Morse estimate for translated points of contactomorphisms of spheres and projective spaces
• On iterated translated points for contactomorphisms of R^{2n+1} and R^{2n} x S^1
• Cup-length estimates for leaf-wise intersections
• Translated points and Rabinowitz Floer homology
• Orderability and the Weinstein Conjecture
• Vanishing of Rabinowitz Floer homology on negative line bundles
• Cuplength estimates in Morse cohomology
• Equivariant wrapped Floer homology and symmetric periodic Reeb orbits
• Bounds for tentacular Hamiltonians
• Coisotropic Ekeland-Hofer capacities
• On a Theorem by Ekeland-Hofer
• Positive loops and $L^{\infty }$-contact systolic inequalities
• Rabinowitz Floer homology of negative line bundles and Floer Gysin sequence
• On a Theorem by Schlenk
• On magnetic leaf-wise intersections
• Barcode entropy for Reeb flows on contact manifolds with Liouville fillings