带慢变角参数摄动平面非Hamilton可积系统的混沌

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基金项目: 国家自然科学基金资助项目(10082003);上海市科技发展基金资助项目(98JC14032);上海市教委科技发展基金资助项目

Chaos in Perturbed Planan Non-Hamiltonian Integrable Systems with Slowly-Varying Angle Parameters

Department of Mechanics, Shanghai University;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China

摘要: 将Melinikov方法推广到带慢变角参数摄动平面可积系统。基于对未受摄动系统几何结构的分析,建立了横截同宿条件。借助常微分方程组解对参数的可微性定理,得到系统的广义Melnikov函数,其简单零点意味着系统可能出现混沌。
- Melinikov方法 /
- 摄动可积系统 /
- 横截同宿 /
- 混沌
Abstract: The Melnikov method was extended to perturbed planan non-Hamiltonian integrable systems with slowly-varying angle parameters.Based on the analysis of the geometric structure of unperturbed systems,the condition of transversely homoclinic intersection was established.The generalized Melnikov function of the perturbed system was presented by applying the theorem on the differentiability of ordinary differential equation solutions with respect to parameters.Chaos may occur in the system if the generalized Melnikov function has simple zeros.
- Melnikov method /
- perturbed integrable system /
- transversely homoclinic /
- chaos

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