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Journal of Fixed Point Theory and Applications

, Volume 10, Issue 1, pp 87–111 | Cite as

Index computations in Rabinowitz Floer homology

  • Will J. Merry
  • Gabriel P. PaternainEmail author
Article

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.

Mathematics Subject Classification (2010)

37C25 53D12 53D40 

Keywords

Morse index Conley–Zehnder index Rabinowitz Floer homology orbit cylinder 

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Copyright information

© Springer Basel AG 2011

Authors and Affiliations

  1. 1.Department of Pure Mathematics and Mathematical StatisticsUniversity of CambridgeCambridgeUK

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