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Bifurcations of Planar Vector Fields and Hilbert's Sixteenth Problem / by Robert Roussarie
(Modern Birkhäuser Classics. ISSN:21971811 ; 164)
版 | 1st ed. 1998. |
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出版者 | (Basel : Springer Basel : Imprint: Birkhäuser) |
出版年 | 1998 |
本文言語 | 英語 |
大きさ | XVII, 206 p : online resource |
著者標目 | *Roussarie, Robert author SpringerLink (Online service) |
件 名 | LCSH:Mathematical analysis LCSH:Global analysis (Mathematics) LCSH:Manifolds (Mathematics) LCSH:Differential equations LCSH:Dynamical systems FREE:Analysis FREE:Global Analysis and Analysis on Manifolds FREE:Differential Equations FREE:Dynamical Systems |
一般注記 | Preface -- 1 Families of Two-dimensional Vector Fields -- 2 Limit Periodic Sets -- 3 The 0-Parameter Case -- 4 Bifurcations of Regular Limit Periodic Sets -- 5 Bifurcations of Elementary Graphics -- 6 Desingularization Theory and Bifurcation of Non-elementary Limit Periodic Sets -- Bibliography -- Index In a coherent, exhaustive and progressive way, this book presents the tools for studying local bifurcations of limit cycles in families of planar vector fields. A systematic introduction is given to such methods as division of an analytic family of functions in its ideal of coefficients, and asymptotic expansion of non-differentiable return maps and desingularisation. The exposition moves from classical analytic geometric methods applied to regular limit periodic sets to more recent tools for singular limit sets. The methods can be applied to theoretical problems such as Hilbert's 16th problem, but also for the purpose of establishing bifurcation diagrams of specific families as well as explicit computations. - - - The book as a whole is a well-balanced exposition that can be recommended to all those who want to gain a thorough understanding and proficiency in recently developed methods. The book, reflecting the state of the art, can also be used for teaching special courses. (Mathematical Reviews) HTTP:URL=https://doi.org/10.1007/978-3-0348-8798-4 |
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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 | 9783034807180 |
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EB00228025 |
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データ種別 | 電子ブック |
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分 類 | LCC:QA299.6-433 DC23:515 |
書誌ID | 4000107335 |
ISBN | 9783034807180 |
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