<電子ブック>
Linear Chaos / by Karl-G. Grosse-Erdmann, Alfred Peris Manguillot
(Universitext. ISSN:21916675)
版 | 1st ed. 2011. |
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出版者 | (London : Springer London : Imprint: Springer) |
出版年 | 2011 |
大きさ | XII, 388 p. 28 illus : online resource |
著者標目 | *Grosse-Erdmann, Karl-G author Peris Manguillot, Alfred author SpringerLink (Online service) |
件 名 | LCSH:Dynamical systems LCSH:Functional analysis LCSH:Operator theory FREE:Dynamical Systems FREE:Functional Analysis FREE:Operator Theory |
一般注記 | Topological dynamics -- Hypercyclic and chaotic operators -- The Hypercyclicity Criterion -- Classes of hypercyclic and chaotic operators -- Necessary conditions for hypercyclicity and chaos -- Connectedness arguments in linear dynamics -- Dynamics of semigroups, with applications to differential equations -- Existence of hypercyclic operators -- Frequently hypercyclic operators -- Hypercyclic subspaces -- Common hypercyclic vectors -- Linear dynamics in topological vector spaces It is commonly believed that chaos is linked to non-linearity, however many (even quite natural) linear dynamical systems exhibit chaotic behavior. The study of these systems is a young and remarkably active field of research, which has seen many landmark results over the past two decades. Linear dynamics lies at the crossroads of several areas of mathematics including operator theory, complex analysis, ergodic theory and partial differential equations. At the same time its basic ideas can be easily understood by a wide audience. Written by two renowned specialists, Linear Chaos provides a welcome introduction to this theory. Split into two parts, part I presents a self-contained introduction to the dynamics of linear operators, while part II covers selected, largely independent topics from linear dynamics. More than 350 exercises and many illustrations are included, and each chapter contains a further ‘Sources and Comments’ section. The only prerequisites are a familiarity with metric spaces, the basic theory of Hilbert and Banach spaces and fundamentals of complex analysis. More advanced tools, only needed occasionally, are provided in two appendices. A self-contained exposition, this book will be suitable for self-study and will appeal to advanced undergraduate or beginning graduate students. It will also be of use to researchers in other areas of mathematics such as partial differential equations, dynamical systems and ergodic theory HTTP:URL=https://doi.org/10.1007/978-1-4471-2170-1 |
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電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
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電子ブック | オンライン | 電子ブック |
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Springer eBooks | 9781447121701 |
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電子リソース |
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EB00197629 |
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