Leaf-wise intersections and Rabinowitz Floer homology
By Peter Albers, Urs Frauenfelder. 2008
89 citations recorded by the source corpus.
In this paper 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 [16].
Subfields: Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/bd631e3ddd877aba4d0140ba249b29d1b3749a7a
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In Applied Mathematics
- E. Shelukhin
- Sheila Sandon
- Michael Usher
- Urs Frauenfelder
- Otto van Koert
- Gabriel P. Paternain
- Peter Albers
- Kai Cieliebak
In Geometry and Topology
- E. Shelukhin
- A. Oancea
- Otto van Koert
- Kai Cieliebak
- Urs Frauenfelder
- Sheila Sandon
- Michael Usher
- Peter Albers
Citations in the corpus
- Boundary depth in Floer theory and its applications to Hamiltonian dynamics and coisotropic submanifolds (2009, background): “J0) by counting, in the familiar way, finite energy solutions to an abstract multivalued perturbation of the equation ∂u ∂s +J˜t s ∂u ∂t −XKτ s (t,u(s,t)) , where now τis allowed to vary freely in [0,1], and uabove contributes to a nonzero matrix element hK[γ−,w−],[γ+,w+]i precisely when u(s,·) → γ”
- Contact geometry of the restricted three‐body problem (2010, methodology): “Thus, work by Albers-Frauenfelder [3, Theorem C] implies the Corollary.”
- A Morse estimate for translated points of contactomorphisms of spheres and projective spaces (2011, methodology): “egard S2n−1 as the unit sphere in R2n. Then its characteristic foliation as a hypersurface of R2n coincides with the Reeb foliation as a contact manifold. By applying Theorem A of Albers-Frauenfelder [AF10] to the special case of S2n−1 we get the following result. Theorem 1.3 ([AF10]). Let ϕ be a Ha”
- The Hofer norm of a contactomorphism (2014, methodology): “Before we continue with the proof of Theorem B we recall some preliminary notions on Rabinowitz-Floer homology [1, 4, 2] and prove several useful auxiliary results.”
- Symplectic homology and the Eilenberg-Steenrod axioms (2015, background): “The dynamical significance of Rabinowitz-Floer homology is that it counts leafwise intersection points of ∂V under Hamiltonian motions [5], and one of its most useful properties is that Hamiltonian displaceability of ∂V (and hence of V ) implies vanishing.”