Please use this identifier to cite or link to this item: https://dspace.upt.ro/xmlui/handle/123456789/4165
Title: On the dynamics of a Hamilton-Poisson system [articol]
Authors: Lăzureanu, Cristian
Petrişor, Camelia
Subjects: Dinamica sistemelor
Stabilitate
Hamilton-Poisson dynamics
Energy-Casimir mapping
Stability
Periodic orbits
Heteroclinic orbits
Mid-point rule
Issue Date: 2018
Publisher: Timişoara : Editura Politehnica
Citation: Lăzureanu, Cristian. On the dynamics of a Hamilton-Poisson system. Timişoara: Editura Politehnica, 2018
Series/Report no.: Buletinul ştiinţific al Universităţii „Politehnica” din Timişoara, România. Seria matematică - fizică, Vol. 63(77), issue 2 (2018), p. 14-28
Abstract: 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.
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