囚禁离子系统的可积性
Integrability of the Trapped Ionic System
摘要：
本文研究了在有理对称六极场和八极场叠加的四极场中的二维囚禁离子系统的亚纯可积性。我们使用的李雅普诺夫和Ziglin-Morales-Ruiz-Ramis的经典方法的证明。研究了Heun方程的正规变分方程（NVE）的单值群的交换性.研究中使用了超越数理论中的一些经典和现代的结果。
英文摘要：
In this paper we will explore the 2D system describing trapped ionic system in the quadrapole field with a superposition of rationally symmetric hexapole and octopole fields for meromorphic integrability. We use the Lyapunov's and Ziglin-Morales-Ruiz-Ramis's classical methods for the proofs. The monodromy group of the normal variational equation (NVE), which is a Heun equation, is studied for commutativity. Some classical and modern results from the theory of transcendental numbers are used for the research.
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