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April  2010, 4(2): 329-357. doi: 10.3934/jmd.2010.4.329

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, South Korea

Received  January 2010 Revised  May 2010 Published  August 2010

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.
Keywords: spectral invariants., global Hamiltonian perturbations, Rabinowitz-Floer homology, Leafwise intersections.
Mathematics Subject Classification: Primary: 53D40; Secondary: 37J10, 58J0.
Citation: Peter Albers, Urs Frauenfelder. Spectral invariants in Rabinowitz-Floer homology and global Hamiltonian perturbations. Journal of Modern Dynamics, 2010, 4 (2) : 329-357. doi: 10.3934/jmd.2010.4.329
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