Journal of Modern Dynamics (JMD)

Spectral invariants in Rabinowitz-Floer homology and global Hamiltonian perturbations

Pages: 329 - 357, Issue 2, April 2010      doi:10.3934/jmd.2010.4.329

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Peter Albers - Purdue University, Department of Mathematics, 150 N. University Street, West Lafayette, IN 47907-2067, United States (email)
Urs Frauenfelder - Department of Mathematics and Research Institute of Mathematics, Seoul National University, San56-1 Shinrim-dong Kwanak-gu Seoul 151- 747, South Korea (email)

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.

Keywords:  Leafwise intersections, Rabinowitz-Floer homology, global Hamiltonian perturbations, spectral invariants.
Mathematics Subject Classification:  Primary: 53D40; Secondary: 37J10, 58J05.

Received: January 2010;      Revised: May 2010;      Available Online: August 2010.