Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System

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...

Full description

Bibliographic Details
Main Author:	Cristian Lăzureanu
Format:	Article
Language:	English
Published:	Hindawi Limited 2017-01-01
Series:	Advances in Mathematical Physics
Online Access:	http://dx.doi.org/10.1155/2017/4596951

id	doaj-9051f22daf4f4f6f96651c87d9add574
record_format	Article
spelling	doaj-9051f22daf4f4f6f96651c87d9add5742021-07-02T06:41:43ZengHindawi LimitedAdvances in Mathematical Physics1687-91201687-91392017-01-01201710.1155/2017/45969514596951Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake SystemCristian Lăzureanu0Department of Mathematics, Politehnica University of Timişoara, Piaţa Victoriei No. 2, 300006 Timişoara, RomaniaIntegrable 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.http://dx.doi.org/10.1155/2017/4596951
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Cristian Lăzureanu
spellingShingle	Cristian Lăzureanu Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System Advances in Mathematical Physics
author_facet	Cristian Lăzureanu
author_sort	Cristian Lăzureanu
title	Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System
title_short	Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System
title_full	Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System
title_fullStr	Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System
title_full_unstemmed	Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System
title_sort	hamilton-poisson realizations of the integrable deformations of the rikitake system
publisher	Hindawi Limited
series	Advances in Mathematical Physics
issn	1687-9120 1687-9139
publishDate	2017-01-01
description	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.
url	http://dx.doi.org/10.1155/2017/4596951
work_keys_str_mv	AT cristianlazureanu hamiltonpoissonrealizationsoftheintegrabledeformationsoftherikitakesystem
_version_	1721336940011192320

Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System

Similar Items