基本解释：KAM理论
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The forced vibration characteristic of a single Degree of freedom 1/4 hysteretic nonlinearity vehicle suspension system under multi-frequency excitation is studied by the period-energy relationship of direct two-dimensional Hamilton system and KAM theory.结合顺行平面Hamilton系统周期-能量关系和KAM理论,研究滞后非线性单自由度1/4车辆悬架系统多频激励下的受扰振动问题,给出两种初值条件下系统受扰固有周期运动的理论解析,证明了系统存在安全的拟周期状态。
In this paper,we prove the existence of plenty of quasi-periodic soltuions for the higher dimensional Laplace equations with constant potential m>2 and Fourier multiplier M_ξ△u+(m+M_ξ)u+u~3=0, subject to periodic boundary conditions via KAM theory.本文利用KAM理论,证明了一类带有常位势m(m>2)以及Fourier乘子M_ξ的高维Laplace方程△u+(m+M_ξ)u+u~3=0,在周期边值条件下拟周期解的存在性。
The classical KAM theory which is constructed by three famous mathematicians Kolmogorov.本文主要研究无穷维KAM理论在偏微分方程中的应用。
In this paper we use knowledge from weak KAM theory and combine with analysis,topology and calculus of variations to Study the relation which is between the Peierls barrier,Ma(?) critical action and viscosity solutions of the time periodic Hamilton-Jacobi equation.本文利用弱KAM理论,结合分析、拓扑及变分等数学工具,研究Peierls障碍函数和Ma(?)临界作用函数与时间周期的哈密顿-雅克比方程的粘性解之间的关系。
In this paper,by using variational analysis and weak KAM theory,we study the behavior of the energy function and investigate the property of the viscosity solutions of time-periodic Hamilton-Jacobi equations.利用变分学和弱KAM理论中的有关知识,研究能量函数的行为,讨论了时间周期的哈密顿—雅克比方程的粘性解的有关性质,推广了Fathi和Siconolfi的结果。
The KAM theory can be used to describe the motions of the double pendulum if the gravitation is treated as a perturbation.建立了用具有质量的刚杆连接的双摆运动方程 ,并将重力作为扰动 ,利用 KAM定理研究了双摆的运动规律 。
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