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...
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| Format: | Article |
| Language: | English |
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Wiley
2017-01-01
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| Series: | Advances in Mathematical Physics |
| Online Access: | http://dx.doi.org/10.1155/2017/4596951 |
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| author | Cristian Lăzureanu |
| author_facet | Cristian Lăzureanu |
| author_sort | Cristian Lăzureanu |
| collection | DOAJ |
| 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. |
| format | Article |
| id | doaj-art-9051f22daf4f4f6f96651c87d9add574 |
| institution | Kabale University |
| issn | 1687-9120 1687-9139 |
| language | English |
| publishDate | 2017-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Advances in Mathematical Physics |
| spelling | doaj-art-9051f22daf4f4f6f96651c87d9add5742025-02-03T01:30:30ZengWileyAdvances 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 |
| spellingShingle | Cristian Lăzureanu Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System Advances in Mathematical Physics |
| title | 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_short | Hamilton-Poisson Realizations of the Integrable Deformations of the Rikitake System |
| title_sort | hamilton poisson realizations of the integrable deformations of the rikitake system |
| url | http://dx.doi.org/10.1155/2017/4596951 |
| work_keys_str_mv | AT cristianlazureanu hamiltonpoissonrealizationsoftheintegrabledeformationsoftherikitakesystem |