Homogeneous bi-Hamiltonian structures and integrable contact systems
arXiv:2502.17269 · doi:10.1142/S2972458925500078
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.
7 pages, to appear on the proceedings of the International Conference on Geometric Science of Information 2025 (GSI 25)