The Study on the Phase Structure of the Paul Trap System

• 作者: Abdellah Rezzouk Ahmed Sali Jaouad Kharbach Mohamed Benkhali Mohamed Benmalek Mohammed Ouazzani-Jamil
• 来源期刊: 应用数学(英文)
• 学科: 数学
• 关键词: HAMILTONIAN SYSTEM INTEGRABILITY Bifurcation LIOUVILLE TORI Periodic Solutions POINCARÉ Section Chaos
• 年，卷（期）: 2017,（4）
• 页码范围: 525-536
• 页数: 12页
• 分类号: O1

摘要

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.