A Relative Poincaré-Birkhoff theorem

Agustin Moreno; Arthur Limoge

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arXiv · 2408.06919

A Relative Poincaré-Birkhoff theorem

Agustin Moreno·Arthur Limoge

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Abstract

In arXiv:2011.06562, the first author and Otto van Koert proved a generalized 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 the twist condition introduced in arXiv:2011.06562 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.

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Agustin Moreno, Arthur Limoge. 2025-01-09. A Relative Poincaré-Birkhoff theorem. https://arxiv.org/abs/2408.06919

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