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arXiv · 2502.17269

Homogeneous bi-Hamiltonian structures and integrable contact systems

Leonardo Colombo·Manuel de León·María Emma Eyrea Irazú·Asier López-Gordón
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Abstract

Bi-Hamiltonian structures can be utilised to compute a maximal set of functions in involution for certain integrable systems, given by the eigenvalues of the recursion operator relating both Poisson structures. We show that the recursion operator relating two compatible Jacobi structures cannot produce a maximal set of functions in involution. However, as we illustrate with an example, bi-Hamiltonian structures can still be used to obtain a maximal set of functions in involution on a contact manifold, at the cost of symplectisation.

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Leonardo Colombo, Manuel de León, María Emma Eyrea Irazú, Asier López-Gordón. 2025-02-24. Homogeneous bi-Hamiltonian structures and integrable contact systems. https://doi.org/10.1142/s2972458925500078

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