2025/04/14 by Ghosh, Aritra, Ghose-Choudhury, Anindya, Guha, Partha · 1 citation
#Chaotic Dynamics (nlin.CD) #Dynamical Systems (math.DS) #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2504.10729
We present novel Hamiltonian descriptions of some three-dimensional systems including two well-known systems describing the three-wave-interaction problem and some well-known chaotic systems, namely, the Chen, Lü, and Qi systems. We show that all of these systems can be described in a Hamiltonian framework in which the Poisson matrix J is supplemented by a resistance matrix R. While such resistive-Hamiltonian systems are manifestly non-conservative, we construct higher-degree Poisson matrices via the Jordan product as N = J R + R J, thereby leading to new bi-Hamiltonian systems. Finally, we discuss conformal Hamiltonian dynamics on Poisson manifolds and demonstrate that by appropriately choosing the underlying parameters, the reduced three-wave-interaction model as well as the Chen and Lü systems can be described in this manner where the concomitant non-conservative part of the dynamics is described with the aid of the Euler vector field.