Homogeneous bi-Hamiltonian structures and integrable contact systems

2025/02/24 by Leonardo Colombo, Colombo, Leonardo, Manuel de León +5
Environmental Science · Physics and Astronomy · #37J35 #37J55 #70H06 #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Methane Hydrates and Related Phenomena #Nonlinear Waves and Solitons #Quantum chaos and dynamical systems #Symplectic Geometry (math.SG)

paper · pdf · doi:10.48550/arxiv.2502.17269

openalex publication_date 2025/02/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Related

• Poisson brackets with prescribed family of functions in involution
• Jacobi Hamiltonian Integrators
• Local bi-integrability of bi-Hamiltonian systems via bi-Poisson reduction
• Integrable systems associated with the Bruhat Poisson structures
• Prop profile of bi-Hamiltonian structures