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Bounds for tentacular Hamiltonians

Federica Pasquotto

Department of Mathematics, Vrije Universiteit Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands

E-mail Address: f.pasquotto@vu.nl

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and

Jagna Wiśniewska

Department of Mathematics, ETH Zürich, Raemistrasse 101, 8092 Zürich, Switzerland

E-mail Address: jagna.wisniewska@math.ethz.ch

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https://doi.org/10.1142/S179352531950047XCited by:4 (Source: Crossref)

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 $L^{\infty}$ $L^{\infty}$ -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.

Keywords:

AMSC: 53D40, 57R17, 58J05

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