广义Ermakov系统的线性化

Ermakov系统的广义Hamilton结构

Generalized Hamiltonian structures for Ermakov systems

我们构造泊松结构的Ermakov系统，使用Ermakov不变量的哈密顿量。得到了两类Poisson结构，其中一类是退化的，在这种情况下，我们导出了Casimir函数。在某些情况下，Casimir函数的存在可以产生超可积的Ermakov系统。最后，我们的特点的情况下，线性化的运动方程是可能的。

Nonlocal transformations of the Generalized Liénard type equations and dissipative Ermakov-Milne-Pinney systems

We employ the method of nonlocal generalized Sundman transformations to formulate the linearization problem for equations of the generalized Liénard type and show that they may be mapped to equations of the dissipative Ermakov-Milne-Pinney type. We obtain the corresponding new first integrals of these derived equations, this method yields a natural generalization of the construction of Ermakov-Lewis invariant for a time dependent oscillator to (coupled) Liénard and Liénard type equations. We also study the linearization problem for the coupled Liénard equation using nonlocal transformations an…

一类广义Ermakov系统的Lie对称性

On the Lie symmetries of a class of generalized Ermakov systems

将Ermakov系统的对称性分析推广到频率除依赖于时间外还依赖于动力学变量的广义情形。在这个扩展的框架下，一类非线性耦合振子被看作是Hamilton Ermakov系统，并以封闭形式精确求解。

The generalized Ermakov conservative system: A discussion

Using older and recent results on the integrability of two-dimensional (2d) dynamical systems, we prove that the results obtained in a recent publication concerning the 2d generalized Ermakov system can be obtained as special cases of a more general approach. This approach is geometric and can be used to study efficiently similar dynamical systems.

Symmetries and conservation laws for the generalized $n$-dimensional Ermakov system

We revise recent results on the classification of the generalized three-dimensional Hamiltonian Ermakov system. We show that a statement published recently is incorrect, while the solution for the classification problem was incomplete. We present the correct classification for the three-dimensional system by using results which related the background space with the dynamics. Finally, we extend our results for the generalized $n$% -dimensional Hamiltonian Ermakov system.

关于比较方程法（广义WKB法）和广义Ermakov-Pinney方程的注记

Remarks on the method of comparison equations (generalized WKB method) and the generalized Ermakov-Pinney equation

建立了比较方程法（广义WKB法）与Ermakov-Pinney方程之间的联系。本文给出了广义Ermakov-Pinney方程的一种摄动解法，并将其应用于构造具有转向点和不具有转向点的二阶微分方程的摄动级数.