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 language | English |
|---|---|
| Pages (from-to) | 209-265 |
| Number of pages | 57 |
| Journal | Journal of Topology and Analysis |
| Volume | 121 |
| Issue number | 1 |
| Early online date | 10 Sep 2018 |
| DOIs | |
| Publication status | Published - 2020 |
Keywords
- Aleksandrov's maximum principle
- Morse-Bott action functional
- non-compact hypersurfaces
- Rabinowitz Floer homology
