Rabinowitz Floer homology is the semi-infinite dimensional Morse homology associated to the Rabinowitz action functional used in the pioneering work of Rabinowitz. Gradient flow lines are solutions of a vortex-like equation. In this survey article we describe the construction of Rabinowitz Floer homology and its applic…
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9 results for “Rabinowitz-Floer”
Lecture notes on advanced homology theories.
problem Finding periodic orbits in complex systems.
method Floer and Rabinowitz-Floer homology.
result Advanced mathematical tools for studying periodic orbits.
In this paper we investigate the properties of a semi-linear problem on a spin manifold involving the Dirac operator, through the construction of Rabinowitz-Floer homology groups. We give several existence results for sub-critical and critical non-linearities as application of the computation of the different homologie…
In this paper, we construct a Rabinowitz-Floer type homology for a class of non-linear problems having a \emph{starshaped} potential; we consider some equivariant cases as well. We give an explicit computation of the homology and we apply it to obtain results of existence and multiplicity of solutions for several model…
We give a definition of symplectic homology for pairs of filled Liouville cobordisms, and show that it satisfies analogues of the Eilenberg-Steenrod axioms except for the dimension axiom. The resulting long exact sequence of a pair generalizes various earlier long exact sequences such as the handle attaching sequence, …
In this paper, we construct the Rabinowitz-Floer homology for the coupled Dirac system \begin{equation*} \left\{ \begin{aligned} Du=\frac{\partial H}{\partial v}(x,u,v)\hspace{4mm} {\rm on} \hspace{2mm}M,\\ Dv=\frac{\partial H}{\partial u}(x,u,v)\hspace{4mm} {\rm on} \hspace{2mm}M, \end{aligned} \right. \end{equation*}…
In this article we consider a variant of Rabinowitz Floer homology in order to define a homological count of discriminant points for paths of contactomorphisms. The growth rate of this count can be seen as an analogue of Givental's nonlinear Maslov index. As an application we prove a Bott-Samelson type obstruction theo…
We construct the TQFT on symplectic cohomology and wrapped Floer cohomology, possibly twisted by a local system of coefficients, and prove that the TQFT respects Viterbo restriction maps and the canonical maps from ordinary cohomology. We also construct the module structure of wrapped Floer cohomology over symplectic c…
The paper explores the correspondence between gradient flow lines of a function and its Lagrange multiplier functional.
problem Detecting critical points of a function subject to constraints.
method Adiabatic limit technique and singular version of the implicit function theorem.
result A one-to-one correspondence between gradient flow lines connecting critical points of Morse index difference one.