Spectral invariants in Rabinowitz-Floer homology and global Hamiltonian perturbations

Peter Albers; Urs Frauenfelder

doi:10.3934/jmd.2010.4.329

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2010, Volume 4, Issue 2: 329-357. Doi: 10.3934/jmd.2010.4.329

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Spectral invariants in Rabinowitz-Floer homology and global Hamiltonian perturbations

Peter Albers^1, and
Urs Frauenfelder^2,

1.
Purdue University, Department of Mathematics, 150 N. University Street, West Lafayette, IN 47907-2067
2.
Department of Mathematics and Research Institute of Mathematics, Seoul National University, San56-1 Shinrim-dong Kwanak-gu Seoul 151- 747

Received: December 31, 2009

Revised: April 30, 2010

Published: July 2010

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Abstract

Spectral invariants were introduced in Hamiltonian Floer homology by Viterbo [26], Oh [20, 21], and Schwarz [24]. We extend this concept to Rabinowitz--Floer homology. As an application we derive new quantitative existence results for leafwise intersections. The importance of spectral invariants for this application is that spectral invariants allow us to derive existence of critical points of the Rabinowitz action functional even in degenerate situations where the functional is not Morse.

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Mathematics Subject Classification: Primary: 53D40; Secondary: 37J10, 58J05.

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