2019/06/06 by Cristian Lăzureanu, Lazureanu, Cristian, Camelia Petrişor +1
Mathematics · Physics and Astronomy · #65D30 #70H12 #70H14 #70K20 #70K42 #70K44 #Advanced Differential Geometry Research #Advanced Topics in Algebra #Dynamical Systems (math.DS) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Nonlinear Waves and Solitons
paper · pdf · doi:10.48550/arxiv.1906.02794
openalex publication_date 2019/06/06 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The dynamics of a three-dimensional Hamilton-Poisson system is closely related to its constants of motion, the energy or Hamiltonian function H and a Casimir C of the corresponding Lie algebra. The orbits of the system are included in the intersection of the level sets H=constant and C=constant. Furthermore, for some three-dimensional Hamilton-Poisson systems, connections between the associated energy-Casimir mapping (H,C) and some of their dynamic properties were reported. In order to detect new connections, we construct a Hamilton-Poisson system using two smooth functions as its constants of motion. The new system has infinitely many Hamilton-Poisson realizations. We study the stability of the equilibrium points and the existence of periodic orbits. Using numerical integration we point out four pairs of heteroclinic orbits.