Homogeneous bi-Hamiltonian structures and integrable contact systems
Mathematical Physics
2025-11-25 v2 math.MP
Symplectic Geometry
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.
Keywords
Cite
@article{arxiv.2502.17269,
title = {Homogeneous bi-Hamiltonian structures and integrable contact systems},
author = {Leonardo Colombo and Manuel de León and María Emma Eyrea Irazú and Asier López-Gordón},
journal= {arXiv preprint arXiv:2502.17269},
year = {2025}
}
Comments
7 pages, to appear on the proceedings of the International Conference on Geometric Science of Information 2025 (GSI 25)