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arXiv · 2504.16169

Symplectic approach to global stability

Verónica Errasti Díez·Jordi Gaset Rifà·Manuel Lainz
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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.

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Verónica Errasti Díez, Jordi Gaset Rifà, Manuel Lainz. 2025-04-22. Symplectic approach to global stability. https://doi.org/10.1007/978-3-032-03924-8_33

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