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The Study on the Phase Structure of the Paul Trap System
Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
Université Privée de Fès, Laboratoire Systèmes et Environnements Durables, Lot. Quaraouiyine Route Ain Chkef, Fès, Morocco
- 1 Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
- 2 Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
- 3 Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
- 4 Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
- 5 Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco
- 6 Université Privée de Fès, Laboratoire Systèmes et Environnements Durables, Lot. Quaraouiyine Route Ain Chkef, Fès, Morocco
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Abstract
In this article, the classic dynamic of Paul trap problem is investigated. We give a complete description of the topological structure of Hamiltonian flows on the real phase space. Using the surgery’s theory of Fomenko Liouville tori, all generic bifurcations of the common level sets of the first integrals were described theoretically. We give also an explicit periodic solution for singular values of the first integrals. Numerical investigations are carried out for all generic bifurcations and we observe order-chaos transition when the critical value of a control parameter is varied.
KeywordsHamiltonian SystemIntegrabilityBifurcationLiouville ToriPeriodic SolutionsPoincaréSectionChaos
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