Symplectic approach to global stability
Mathematical Physics
2025-10-28 v2 High Energy Physics - Theory
math.MP
Abstract
We present a new approach to the problem of proving global stability, based on symplectic geometry and with a focus on systems with several conserved quantities. We also provide a proof of instability for integrable systems whose momentum map is everywhere regular. Our results take root in the recently proposed notion of a confining function and are motivated by ghost-ridden systems, for whom we put forward the first geometric definition.
Keywords
Cite
@article{arxiv.2504.16169,
title = {Symplectic approach to global stability},
author = {Verónica Errasti Díez and Jordi Gaset Rifà and Manuel Lainz},
journal= {arXiv preprint arXiv:2504.16169},
year = {2025}
}
Comments
7 pages, plus references. v2: Journal version