光滑遍歷理論導論 (影印版) 9787040611991 (葡)路易斯.巴雷拉(Luis Barreira)(美)亞
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物品所在地：中國大陸
原出版社：高等教育
物品所在地：中國大陸
原出版社：高等教育
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| *完成訂單後正常情形下約兩周可抵台。 *本賣場提供之資訊僅供參考，以到貨標的為正確資訊。 印行年月：202402*若逾兩年請先於私訊洽詢存貨情況，謝謝。 台灣(台北市)在地出版社，每筆交易均開具統一發票，祝您中獎最高1000萬元。 書名：光滑遍歷理論導論 (影印版) ISBN：9787040611991 出版社：高等教育 著編譯者：(葡)路易斯.巴雷拉(Luis Barreira)(美)亞 叢書名：美國數學會經典影印系列 頁數：304 所在地：中國大陸 *此為代購商品 書號：1628661 可大量預訂，請先連絡。 【台灣高等教育出版社簡體書】 光滑遍歷理論導論 (影印版) 787040611991 (葡)路易斯.巴雷拉(Luis Barreira)(美)亞 內容簡介 本書是關於光滑遍歷理論的首次系統介紹。它由兩部分組成：第一部分介紹了理論核心，第二部分討論了更高級的主題。特別是，書中描述了Lyapunov指數的一般理論及其在微分方程穩定性理論中的應用、非均勻雙曲性的概念、穩定流形理論（著重介紹不變葉狀結構的絕對連續性）以及具有非零Lyapunov指數的動力系統的遍歷理論。作者還詳細描述了所有具有非零Lyapunov指數的保守系統的基本例子，包括在非正曲率緊曲面上的測地線流。 本書是Lyapunov Exponents and Smooth Ergodic Theory的修訂和大幅擴展版，面向專攻動力系統和遍歷理論的研究生，以及任何想要掌握光滑遍歷理論並學會使用其工具的人士。本書設有80多個練習題，可用作光滑遍歷理論高級課程的主要教材。本書內容自封，讀者只需要基本的實分析、測度論、微分方程和拓撲學的知識，即便如此，作者仍然提供了讀者所需的背景定義和結果。目錄 PrefacePart 1 The Core of the Theory Chapter 1 Examples of Hyperbolic Dynamical Systems §1 1 Anosov diffeomorphisms §1 2 Anosov flows §1 3 The Katok map of the 2-torus §1 4 Diffeomorphisms with nonzero Lyapunov exponents on surfaces §1 5 A flow with nonzero Lyapunov exponents Chapter 2 General Theory of Lyapunov Exponents §2 1 Lyapunov exponents and their basic properties §2 2 The Lyapunov and Perron regularity coefficients §2 3 Lyapunov exponents for linear differential equations §2 4 Forward and backward regularity The Lyapunov-Perron regularity §2 5 Lyapunov exponents for sequences of matrices Chapter 3 Lyapunov Stability Theory of Nonautonomous Equations §3 1 Stability of solutions of ordinary differential equations §3 2 Lyapunov absolute stability theorem §3 3 Lyapunov conditional stability theorem Chapter 4 Elements of the Nonuniform Hyperbolicity Theory §4 1 Dynamical systems with nonzero Lyapunov exponents §4 2 Nonuniform complete hyperbolicity §4 3 Regular sets §4 4 Nonuniform partial hyperbolicity §4 5 HSlder continuity of invariant distributions Chapter 5 Cocycles over Dynamical Systems §5 1 Cocycles and linear extensions §5 2 Lyapunov exponents and Lyapunov-Perron regularity for cocycles §5 3 Examples of measurable cocycles over dynamical systems Chapter 6 The Multiplicative Ergodic Theorem §6 1 Lyapunov-Perron regularity for sequences of triangular matrices §6 2 Proof of the Multiplicative Ergodic Theorem §6 3 Normal forms of measurable cocycles §6 4 Lyapunov charts Chapter 7 Local Manifold Theory §7 1 Local stable manifolds §7 2 An abstract version of the Stable Manifold Theorem §7 3 Basic properties of stable and unstable manifolds Chapter 8 Absolute Continuity of Local Manifolds §8 1 Absolute continuity of the holonomy map §8 2 A proof of the absolute continuity theorem §8 3 Computing the Jacobian of the holonomy map §8 4 An invariant foliation that is not absolutely continuous Chapter 9 Ergodic Properties of Smooth Hyperbolic Measures §9 1 Ergodicity of smooth hyperbolic measures §9 2 Local ergodicity §9 3 The entropy formula Chapter 10 Geodesic Flows on Surfaces of Nonpositive Curvature §10 1 Preliminary information from Riemannian geometry §10 2 Definition and local properties of geodesic flows §10 3 Hyperbolic properties and Lyapunov exponents §10 4 Ergodic properties §10 5 The entropy formula for geodesic flows Part 2 Selected Advanced Topics Chapter 11 Cone Technics §11 1 Introduction §11 2 Lyapunov functions §11 3 Cocycles with values in the symplectic group Chapter 12 Partially Hyperbolic Diffeomorphisms with Nonzero Exponents §12 1 Partial hyperbolicity §12 2 Systems with negative central exponents §12 3 Foliations that are not absolutely continuous Chapter 13 More Examples of Dynamical Systems with Nonzero Lyapunov Exponents §13 1 Hyperbolic diffeomorphisms with countably many ergodic components §13 2 The Shub-Wilkinson map Chapter 14 Anosov Rigidity §14 1 The Anosov rigidity phenomenon I §14 2 The Anosov rigidity phenomenon II Chapter 15 C1 Pathological Behavior: Pugh's Example Bibliography Index 詳細資料或其他書籍請至台灣高等教育出版社查詢，查後請於PChome商店街私訊告知ISBN或書號，我們即儘速上架。 |
