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連續(xù)和離散動力系統(tǒng)引論(第二版 影印版)

連續(xù)和離散動力系統(tǒng)引論(第二版 影印版)

定 價:¥199.00

作 者: R. Clark Robinson
出版社: 高等教育出版社
叢編項:
標(biāo) 簽: 暫缺

ISBN: 9787040470093 出版時間: 2017-04-01 包裝:
開本: 頁數(shù): 733 字?jǐn)?shù):  

內(nèi)容簡介

  本書從數(shù)學(xué)的角度初步介紹了定性微分方程和離散動力系統(tǒng),包括了理論性證明、計算方法和應(yīng)用。全書分兩部分,即微分方程的連續(xù)時間和動力系統(tǒng)的離散時間,可分別用于一學(xué)期的課程, 或兩者結(jié)合為一年期的課程。微分方程的素材通過任意維數(shù)的線性系統(tǒng)介紹了定性的或幾何的方法。接下來的幾章中平衡性是*重要的特點(diǎn),其中標(biāo)量(能量) 函數(shù)為主要工具,在那里出現(xiàn)了周期軌道,*后還討論了微分方程的混沌系統(tǒng)。通過例題和定理引進(jìn)了許多不同的方法。離散動力系統(tǒng)的素材是從單變量的映射著手的,然后繼續(xù)進(jìn)到高維體系中。處理論題則從具有明顯的周期點(diǎn)的例子開始, 然后對那些可證明它們存在但不能給出顯式形式的分析引進(jìn)了符號動力學(xué)?;煦缦到y(tǒng)既可數(shù)學(xué)地表示也可用更具計算性的Lyapunov 指數(shù)表示。以一維映射為模型,多重映射則被用來講述高維的同一素材。這個高維素材不那么具有可計算性,而是更具概念性和理論性。關(guān)于分形的*后一章引進(jìn)了各種維數(shù),它是度量一個系統(tǒng)復(fù)雜性的另一個計算工具。它也處理了迭代函數(shù)系統(tǒng),其給出了復(fù)雜集合的例子。在此書的第二版中,許多素材已被重寫以使表述更清楚。另外,書的兩部分都添進(jìn)了一些新的材料。此書可以用作大學(xué)高年級的常微分方程和/或動力系統(tǒng)課程的教科書。預(yù)備知識是微積分的標(biāo)準(zhǔn)課程(單變量和多變量的)、線性代數(shù)和微分方程初階。

作者簡介

暫缺《連續(xù)和離散動力系統(tǒng)引論(第二版 影印版)》作者簡介

圖書目錄

Preface Historical Prologue Part 1. Systems of Nonlinear Differential Equations Chapter 1. Geometric Approach to Differential Equations Chapter 2. Linear Systems 2.1. Fundamental Set of Solutions Exercises 2.1 2.2. Constant Coefficients: Solutions and Phase Portraits Exercises 2.2 2.3. Nonhomogeneous Systems: Time-dependent Forcing Exercises 2.3 2.4. Applications Exercises 2.4 2.5. Theory and Proofs Chapter 3. The Flow: Solutions of Nonlinear Equations 3.1. Solutions of Nonlinear Equations Exercises 3.1 3.2. Numerical Solutions of Differential Equations Exercises 3.2 3.3. Theory and Proofs Chapter 4. Phase Portraits with Emphasis on Fixed Points 4.1. Limit Sets Exercises 4.1 4.2. Stability of Fixed Points Exercises 4.2 4.3. Scalar Equations Exercises 4.3 4.4. Two Dimensions and Nullclines Exercises 4.4 4.5. Linearized Stability of Fixed Points Exercises 4.5 4.6. Competitive Populations Exercises 4.6 4.7. Applications Exercises 4.7 4.8. Theory and Proofs Chapter 5. Phase Portraits Using Scalar Functions 5.1. Predator-Prey Systems Exercises 5.1 5.2. Undamped Forces Exercises 5.2 5.3. Lyapunov Functions for Damped Systems Exercises 5.3 5.4. Bounding Functions Exercises 5.4 5.5. Gradient Systems Exercises 5.5 5.6. Applications Exercises 5.6 5.7. Theory and Proofs Chapter 6. Periodic Orbits 6.1. Introduction to Periodic Orbits Exercises 6.1 6.2. Poincare-Bendixson Theorem Exercises 6.2 6.3. Self-Excited Oscillator Exercises 6.3 6.4. Andronov-HopfBifurcation Exercises 6.4 6.5. Homoclinic Bifurcation Exercises 6.5 6.6. Rate of Change of Volume Exercises 6.6 6.7. Poincare Map Exercises 6.7 6.8. Applications Exercises 6.8 6.9. Theory and Proofs Chapter 7. Chaotic Attractors 7.1. Attractors Exercises 7.1 7.2. Chaotic Attractors Exercise 7.2 7.3. Lorenz System Exercises 7.3 7.4. RSssler Attractor Exercises 7.4 7.5. Forced Oscillator Exercises 7.5 7.6. Lyapunov Exponents Exercises 7.6 7.7. Test for Chaotic Attractors Exercises 7.7 7.8. Applications 7.9. Theory and Proofs Part 2. Iteration of Functions Chapter 8. Iteration of Functions as Dynamics 8.1. One-Dimensional Maps 8.2. Functions with Several Variables Chapter 9. Periodic Points of One-Dimensional Maps 9.1. Periodic Points Exercises 9.1 9.2. Iteration Using the Graph Exercises 9.2 9.3. Stability of Periodic Points Exercises 9.3 9.4. Critical Points and Basins Exercises 9.4 9.5. Bifurcation of Periodic Points Exercises 9.5 9.6. Conjugacy Exercises 9.6 9.7. Applications Exercises 9.7 9.8. Theory and Proofs Chapter 10. Itineraries for One-Dimensional Maps 10.1. Periodic Points from Transition Graphs Exercises 10.1 10.2. Topological Transitivity Exercises 10.2 10.3. Sequences of Symbols Exercises 10.3 10.4. Sensitive Dependence on Initial Conditions Exercises 10.4 10.5. Cantor Sets Exercises 10.5 10.6. Piecewise Expanding Maps and Subshifts Exercises 10.6 10.7. Applications Exercises 10.7 10.8. Theory and Proofs Chapter 11. Invariant Sets for One-Dimensional Maps 11.1. Limit Sets Exercises 11.1 11.2. Chaotic Attractors Exercises 11.2 11.3. Lyapunov Exponents Exercises 11.3 11.4. Invariant Measures Exercises 11.4 11.5. Applications 11.6. Theory and Proofs Chapter 12. Periodic Points of Higher Dimensional Maps 12.1. Dynamics of Linear Maps Exercises 12.1 12.2. Classification of Periodic Points Exercises 12.2 12.3. Stable Manifolds Exercises 12.3 12.4. Hyperbolic Toral Automorphisms Exercises 12.4 12.5. Applications Exercises 12.5 12.6. Theory and Proofs Chapter 13. Invariant Sets for Higher Dimensional Maps 13.1. Geometric Horseshoe Exercises 13.1 13.2. Symbolic Dynamics Exercises 13.2 13.3. Homoclinic Points and Horseshoes Exercises 13.3 13.4. Attractors Exercises 13.4 13.5. Lyapunov Exponents Exercises 13.5 13.6. Applications 13.7. Theory and Proofs Chapter 14. Fractals 14.1. Box Dimension Exercises 14.1 14.2. Dimension of Orbits Exercises 14.2 14.3. Iterated-Function Systems Exercises 14.3 14.4. Theory and Proofs Appendix A. Background and Terminology A.1. Calculus Background and Notation A.2. Analysis and Topology Terminology A.3. Matrix Algebra Appendix B. Generic Properties Bibliography Index

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