Geometrical Methods in the Theory of Ordinary Differential Equations
Geometrical Methods in the Theory of Ordinary Differential Equations
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DOI：
10.1007/978-1-4612-1037-5
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发表时间：
1983
期刊：
影响因子：
--
通讯作者：
V. Arnold
中科院分区：
文献类型：
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作者：
V. Arnold
自第一版这本书，几何方法在理论的常微分方程已成为非常受欢迎的，并取得了一些进展，部分与计算机的帮助。大部分这方面的进展是代表在这一修订，扩大版，包括这样的主题作为费根鲍姆普遍性的期间加倍，佐拉代克解决方案，Iljashenko证明，Ecalle和沃罗宁理论，瓦尔琴科和Hovanski定理，和Neistadt理论。在本书的材料选择中，作者解释了适用于微分方程研究的基本思想和方法。为了使基本思想不受过多的技术细节的影响，作出了特别的努力。因此，最基本的问题被认为是非常详细的，而理论中更特殊和困难的部分具有调查的性质。因此，读者只需要一个一般的数学知识，很容易遵循这一文本。它是针对数学家，以及所有用户的理论微分方程。
Since the first edition of this book, geometrical methods in the theory of ordinary differential equations have become very popular and some progress has been made partly with the help of computers. Much of this progress is represented in this revised, expanded edition, including such topics as the Feigenbaum universality of period doubling, the Zoladec solution, the Iljashenko proof, the Ecalle and Voronin theory, the Varchenko and Hovanski theorems, and the Neistadt theory. In the selection of material for this book, the author explains basic ideas and methods applicable to the study of differential equations. Special efforts were made to keep the basic ideas free from excessive technicalities. Thus the most fundamental questions are considered in great detail, while of the more special and difficult parts of the theory have the character of a survey. Consequently, the reader needs only a general mathematical knowledge to easily follow this text. It is directed to mathematicians, as well as all users of the theory of differential equations.