arXiv subjects

Jagna Wiśniewska

Publications and source records attributed to Jagna Wiśniewska.

5 recordsLinked to original sources

arXiv2026

Two-boost problem for the rotating Kepler problem

The two-boost problem in space mission design asks whether two points of phase space can be connected with the help of two boosts of given energy. In this article we provide a positive answer for the rotating Kepler problem by generalizing the definition of Lagrangian Rabinowitz Floer homology from the class introduced in [4] to a strictly broader class, and computing the corresponding homology in this more general setting. The principal technical challenge is the non-compactness of the energy hypersurface both near the collision singularity and in the infinity.

math.SG↗

arXiv2026

Two-boost problem for the Newtonian potential at the infinity

The two-boost problem in space mission design asks whether two points of position space can be connected by a Hamiltonian path on a fixed energy level set. We provide a positive answer for a class of systems having the same behaviour at infinity as the restricted three-body problem by relating it to the Lagrangian Rabinowitz Floer homology computed in [4]. The main technical challenge is to prove the boundedness of the corresponding sets of Reeb chords.

math.SG↗

arXiv2025

The two-boost problem and Lagrangian Rabinowitz Floer homology

The two-boost problem in space mission design asks whether two points of phase space can be connected with the help of two boosts of given energy. We provide a positive answer for a class of systems related to the restricted three-body problem by defining and computing its Lagrangian Rabinowitz Floer homology. The main technical work goes into dealing with the noncompactness of the corresponding energy hypersurfaces.

math.SG↗

arXiv2020

Computing the Rabinowitz Floer homology of tentacular hyperboloids

We compute the Rabinowitz Floer homology for a class of non-compact hyperboloids $Σ\simeq S^{n+k-1}\times\mathbb{R}^{n-k}$. Using an embedding of a compact sphere $Σ_0\simeq S^{2k-1}$ into the hypersurface $Σ$, we construct a chain map from the Floer complex of $Σ$ to the Floer complex of $Σ_0$. In contrast to the compact case, the Rabinowitz Floer homology groups of $Σ$ are both non-zero and not equal to its singular homology. As a consequence, we deduce that the Weinstein Conjecture holds for any strongly tentacular deformation of such a hyperboloid.

math.SG↗

arXiv2020

Rabinowitz Floer homology for tentacular Hamiltonians

This paper extends the definition of Rabinowitz Floer homology to non-compact hypersurfaces. We present a general framework for the construction of Rabinowitz Floer homology in the non-compact setting under suitable compactness assumptions on the periodic orbits and the moduli spaces of Floer trajectories. We introduce a class of hypersurfaces being the level sets of specific Hamiltonians: strongly tentacular Hamiltonians, for which the compactness conditions are satisfied, thus enabling us to define the Rabinowitz Floer homology for this class. Rabinowitz Floer homology in turn serves as a tool to address the Weinstein conjecture and establish existence of closed characteristics.

math.SG↗