Bounds for tentacular Hamiltonians

Federica Pasquotto*, Jagna Winiewska

*Corresponding author for this work

Research output: Contribution to JournalArticleAcademicpeer-review

Abstract

This paper represents a first step toward the extension of the definition of Rabinowitz Floer homology to non-compact energy hypersurfaces in exact symplectic manifolds. More concretely, we study under which conditions it is possible to establish L∞-bounds for the Floer trajectories of a Hamiltonian with non-compact energy levels. Moreover, we introduce a class of Hamiltonians, called tentacular Hamiltonians which satisfy the conditions: how to define Rabinowitz Floer homology for these examples will be the subject of a follow-up paper.

Original languageEnglish
Pages (from-to)209-265
Number of pages57
JournalJournal of Topology and Analysis
Volume121
Issue number1
Early online date10 Sept 2018
DOIs
Publication statusPublished - 2020

Funding

This work has been supported by the Vrije Competitie Grant 613.001.111 Periodic Motions on Non-Compact Energy Surfaces of NWO. The second author also would like to thank Kai Zehmisch for his kind hospitality at the Westfälische Wilhelms-Universität Münster and for the partial financial support from the Grant SFB/TRR 191 Symplectic Structures in Geometry, Algebra and Dynamics of the DFG.

FundersFunder number
Deutsche Forschungsgemeinschaft
Nederlandse Organisatie voor Wetenschappelijk Onderzoek

    Keywords

    • Aleksandrov's maximum principle
    • Morse-Bott action functional
    • non-compact hypersurfaces
    • Rabinowitz Floer homology

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