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