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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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Symplectic Approach to Global Stability

  • 会议论文

  • 发表日期：

    2026年

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  • Verónica Errasti Díez,
  • Jordi Gaset Rifá,
  • Manuel Lainz Valcázar

摘要

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.