NDLI: Index computations in Rabinowitz Floer homology

Content Provider	Springer Nature Link
Author	Merry, Will J. Paternain, Gabriel P.
Copyright Year	2011
Abstract	In this note we study two index questions. In the first we establish the relationship between the Morse indices of the free time action functional and the fixed time action functional. The second is related to Rabinowitz Floer homology. Our index computations are based on a correction term which is defined as follows: around a nondegenerate Hamiltonian orbit lying in a fixed energy level a well-known theorem says that one can find a whole cylinder of orbits parametrized by the energy. The correction term is determined by whether the periods of the orbits are increasing or decreasing as one moves up the orbit cylinder. We also provide an example to show that, even above the Mañé critical value, the periods may be increasing thus producing a jump in the Morse index of the free time action functional in relation to the Morse index of the fixed time action functional.
Starting Page	87
Ending Page	111
Page Count	25
File Format	PDF
ISSN	16617738
Journal	Journal of Fixed Point Theory and Applications
Volume Number	10
Issue Number	1
e-ISSN	16617746
Language	English
Publisher	SP Birkhäuser Verlag Basel
Publisher Date	2011-04-19
Publisher Place	Basel
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	Morse index Conley–Zehnder index Rabinowitz Floer homology orbit cylinder Fixed points, periodic points, fixed-point index theory Lagrangian submanifolds; Maslov index Floer homology and cohomology, symplectic aspects Mathematics Mathematical Methods in Physics Analysis
Content Type	Text
Resource Type	Article
Subject	Geometry and Topology Applied Mathematics Modeling and Simulation

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