Bounds for tentacular Hamiltonians. (English) Zbl 1440.53101
Summary: 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 \(L^\infty \)-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.
MSC:
| 53D40 | Symplectic aspects of Floer homology and cohomology |
| 57R17 | Symplectic and contact topology in high or arbitrary dimension |
| 58J05 | Elliptic equations on manifolds, general theory |
Keywords:
Rabinowitz Floer homology; non-compact hypersurfaces; Morse-Bott action functional; Aleksandrov’s maximum principleReferences:
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