---
author:
- 'F. Pasquotto and J. Wiśniewska'
---

.8cm

F. Pasquotto [^1], and J. Wiśniewska[^2]

[**Abstract.**]{}

This paper represents a first step towards the extension of the definition of Rabinowitz Floer homology to non-compact energy hypersurfaces $\Sigma$ 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 RFH for these examples will be the subject of a follow-up paper.

=12.5cm

[^1]: *Department of Mathematics, Vrije Universiteit Amsterdam, the Netherlands.*

[^2]: *Department of Mathematics, Westfälische Wilhelms-Universität Münster, Germany.*
