From Euler-Jacobi to Bogoyavlensky and back

2025/03/27 by Murari, Davide, Sansonetto, Nicola
#37J15 #37J35 #37J60 #70H06 #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2503.21950

Abstract

This work focuses on two notions of non-Hamiltonian integrable systems: B-integrability and Euler-Jacobi integrability. We first show that the first notion is stronger. We then investigate which possible "non-evident" properties one can add to the Euler-Jacobi Theorem to make the dynamics B-integrable.

Related

• Non-commutative integrability, exact solvability and the Hamilton-Jacobi theory
• Lectures on integrable Hamiltonian systems
• Non-integrability criterion for homogeneous Hamiltonian systems via blowing-up technique of singularities
• Hamilton-Jacobi theory for Hamiltonian and non-Hamiltonian systems
• Non-integrability of a system with the Dyson Potential