微分方程与动力系统
Differential Equations and Dynamical Systems
Lawrence Perko · 初版 1991 年
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本教材对非线性微分方程与动力系统的定性与几何理论进行了系统性研究。尽管全书的核心主题是非线性系统的局部和全局行为及其分岔，但在开篇对线性系统也作了详尽的阐述。本书涵盖了清晰理解动力系统定性行为所需的全部必备资料，包括 Hartman-Grobman theorem 证明的大纲与图解示例、Poincare map 在……中的运用
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……以前学过分析，但这本书直接又严谨，为我进阶到泛函分析（functional analysis）等内容提供了很好的框架，这是其他书没能给我的准备。2. Lawrence Perko 的《Differential Equations and Dynamical Systems》——帮我巩固了动力系统的行为特征以及求解方法。对我理解控制理论（control theory）也有很大帮助。3. 《A Concise Introduction to the Theory of Integration》……
…analysis in the past, but this book is direct and rigorous and provided a good framework to move forward into things like functional analysis in a way that I was not prepared for with other books. 2. Differential Equations and Dynamical Systems by Lawrence Perko - Solidified for me how dynamic systems behaved and were solved. Very much helped my understanding of control theory as well. 3. A Concise Introduction to the Theory of Integration…
……小球因为不可预测的微扰而开始滚动。微小的运动会根据李雅普诺夫指数（Lyapunov exponent）被放大，在不稳定情况下这个指数很大。Hirsch、Smale 和 Devaney 合著的关于微分方程和动力系统的书是学习这方面内容的好去处。在经典力学中，我们把圆顶顶端建模为一个零直径的点，但真实的物理圆顶是由随机振动的分子构成的，这就会引发……
…ball starts rolling because of an unpredictable perturbation. Small motions are amplified according to the Lyapunov exponent, which in the unstable case is large. Hirsch and Smale and Devaney's book on differential equations and dynamical systems is a good place to learn about this. In classical mechanics we model a zero-diameter point at the top of the dome, but a real physical dome would be made of molecules vibrating randomly and that starts…
我很喜欢 Hirsch 和 Smale 以前写的那本老书，书名大概叫《Linear algebra, differential equations, and dynamical systems》。现在它被加入第三作者的扩充版取代了，书名也更长，虽然我还没翻过，但估计也很棒。我不知道这本 H&S 的书对初学者友不友好，……
I liked Hirsch and Smale's old book called something like "Linear algebra, differential equations, and dynamical systems". It is now replaced by an expanded edition with a 3rd author added and a longer title, that I expect is also good, though I haven't looked at it. I don't know if the H&S book is beginner friendly,…