Author(s)

Jaouad Kharbach¹, Mohamed Benkhali¹, Mohamed Benmalek¹, Ahmed Sali¹, Abdellah Rezzouk¹, Mohammed Ouazzani-Jamil²

¹Laboratoire de Physique du Solide, Faculté des Sciences Dhar El Mahraz, Université Sidi Mohamed Ben Abdellah, Fès-Atlas, Morocco.
²Université Privée de Fès, Laboratoire Systèmes et Environnements Durables, Lot. Quaraouiyine Route Ain Chkef, Fès, Morocco.

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.

Hamiltonian System, Integrability, Bifurcation, Liouville Tori, Periodic Solutions, Poincaré Section, Chaos

Kharbach, J. , Benkhali, M. , Benmalek, M. , Sali, A. , Rezzouk, A. and Ouazzani-Jamil, M. (2017) The Study on the Phase Structure of the Paul Trap System. Applied Mathematics, 8, 525-536. doi: 10.4236/am.2017.84042.