Galois Theory of Linear Differential Equations
Galois Theory of Linear Differential Equations
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DOI：
10.1007/978-3-642-55750-7
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发表时间：
2012-10
期刊：
影响因子：
--
通讯作者：
M. Put;M. Singer
中科院分区：
文献类型：
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作者：
M. Put;M. Singer
线性微分方程构成了本书的中心主题，伽罗瓦理论是统一的主题。介绍了大量的方面：代数理论，特别是微分伽罗瓦理论，形式理论，分类，确定有限项可解性的算法，单调性和希尔伯特第21问题，渐进性和可求和性，反问题和正特性线性微分方程。附录旨在帮助读者了解所使用的概念，包括代数几何、线性代数群、滑轮和所使用的坦纳基范畴。本书将成为该数学领域所有数学家（包括研究生）的标准参考书。
Linear differential equations form the central topic of this volume, Galois theory being the unifying theme. A large number of aspects are presented: algebraic theory especially differential Galois theory, formal theory, classification, algorithms to decide solvability in finite terms, monodromy and Hilbert's 21st problem, asymptotics and summability, the inverse problem and linear differential equations in positive characteristic. The appendices aim to help the reader with concepts used, from algebraic geometry, linear algebraic groups, sheaves, and tannakian categories that are used. This volume will become a standard reference for all mathematicians in this area of mathematics, including graduate students.