Work

A relative Poincaré–Birkhoff theorem

Year: 2026

Type: article

Abstract: A. Moreno and Otto van Koert proved a generalised version of the classical Poincaré–Birkhoff theorem, for Liouville domains of any dimension. In this article, we prove a relative version for Lagrangians with Legendrian boundary. This gives interior chords of arbitrary large length, provided that the twist condition introduced by Moreno and van Koert is satisfied. The motivation comes from finding spatial consecutive collision orbits of arbitrary large length in the spatial circular restricted three‐body problem, which are relevant for gravitational assist in the context of orbital mechanics. This is an application of a local version of wrapped Floer homology, which we introduce as the open string analogue of local Floer homology for closed strings.

Source: Bulletin of the London Mathematical Society

DOI: 10.1112/blms.70426

Authors: Agustin Moreno, Arthur Limoge

Institution: Heidelberg University

Language: English

Topic: Geometric and Algebraic Topology

Subfield: Geometry and Topology

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Estimated APC paid: $3,930

Funder: Air Force Office of Scientific Research