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https://doi.org/10.1063/1.1449957

has been cited by the following article:

• TITLE: The Study on the Phase Structure of the Paul Trap System

  AUTHORS: Jaouad Kharbach, Mohamed Benkhali, Mohamed Benmalek, Ahmed Sali, Abdellah Rezzouk, Mohammed Ouazzani-Jamil

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

  JOURNAL NAME: Applied Mathematics, Vol.8 No.4, April 28, 2017

  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.