Symplectic approach to global stability
arXiv:2504.16169 · doi:10.1007/978-3-032-03924-8_33
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.
7 pages, plus references. v2: Journal version