Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System. (27th August 2017)

• Record Type: Journal Article
• Authors: Lăzureanu, Cristian
• Other Names: Weder Ricardo Academic Editor.
• Is Part Of: Advances in mathematical physics. Volume 2017(2017)
• Publication Date: 2017-08-27
• Subjects: Mathematical physics -- Periodicals; Mathematical physics; Periodicals; 530.15
• DOI: 10.1155/2017/4596951
• Languages: English
• ISSNs: 1687-9120

Abstract

Abstract : Integrable deformations of an integrable case of the Rikitake system are constructed by modifying its constants of motions. Hamilton-Poisson realizations of these integrable deformations are given. Considering two concrete deformation functions, a Hamilton-Poisson approach of the obtained system is presented. More precisely, the stability of the equilibrium points and the existence of the periodic orbits are proved. Furthermore, the image of the energy-Casimir mapping is determined and its connections with the dynamical elements of the considered system are pointed out.