标题： 李系统和微分方程的可积性条件及其一些应用 显示英文标题

标题： Lie systems and integrability conditions of differential equations and some of its applications

摘要： 李群系统几何理论被用来建立若干微分方程系统的可积性条件，特别是某些黎卡提方程和埃姆亚科夫系统。 文献中许多不同的可积性准则将从这一新视角进行分析，并给出一些物理学中的应用。 显示英文摘要

摘要： The geometric theory of Lie systems is used to establish integrability conditions for several systems of differential equations, in particular some Riccati equations and Ermakov systems. Many different integrability criteria in the literature will be analysed from this new perspective, and some applications in physics will be given.