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Integrable systems in cosymplectic geometry

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arxiv 2212.09427 v1 pith:7NPBUXT3 submitted 2022-12-19 math.DG math-phmath.MP

Bozidar Jovanovic , Katarina Lukic This is my paper · ORCID
classification math.DGmath-phmath.MP
keywords cosymplecticmanifoldshamiltonianintegrabilitysystemsaction-anglearnold-liouvilleconstruction
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Motivated by the time-dependent Hamiltonian dynamics, we extend the notion of Arnold-Liouville and noncommutative integrability of Hamiltonian systems on symplectic manifolds to that on cosymplectic manifolds. We prove a variant of the non-commutative integrability for evaluation and Reeb vector fields on cosymplectic manifolds and provide a construction of cosymplectic action-angle variables.

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  1. Contact line bundles, foliations, and integrability

    math.SG 2025-02 conditional novelty 6.0 of 10

    A line-bundle approach to contact integrability unifies cooriented and non-cooriented systems and covers dissipative contact Hamiltonians.

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