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Scaling Laws in Dynamical Systems（英文版）动力系统的标度律

样章
作者：
Edson Denis Leonel
定价：
119.00元
ISBN：
978-7-04-057212-4
版面字数：
460.000千字
开本：
特殊
全书页数：
暂无
装帧形式：
精装
重点项目：
暂无
出版时间：
2022-03-25
读者对象：
学术著作
一级分类：
自然科学
二级分类：
数学与统计
三级分类：
动力系统
暂无
  • 前辅文
  • 1 Introductio
    • 1.1 Initial Concept
    • 1.2 Summar
  • 2 One-Dimensional Mapping
    • 2.1 Introduction
    • 2.2 The Concept of Stability
      • 2.2.1 Asymptotically Stable Fixed Poin
      • 2.2.2 Neutral Stability
      • 2.2.3 Unstable Fixed Poin
    • 2.3 Fixed Points to the LogisticMap
    • 2.4 Bifurcations
      • 2.4.1 Transcritical Bifurcation
      • 2.4.2 Period Doubling Bifurcatio
      • 2.4.3 Tangent Bifurcatio
    • 2.5 Summar
    • 2.6 Exercise
  • 3 Some Dynamical Properties for the Logistic Ma
    • 3.1 Convergence to the Stationary Stat
      • 3.1.1 Transcritical Bifurcation
      • 3.1.2 Period Doubling Bifurcatio
      • 3.1.3 Route to Chaos via Period Doublin
      • 3.1.4 Tangent Bifurcatio
    • 3.2 Lyapunov Exponen
    • 3.3 Summar
    • 3.4 Exercise
  • 4 The Logistic-Like Map
    • 4.1 The Mappin
    • 4.2 Transcritical Bifurcatio
      • 4.2.1 Analytical Approach to Obtain α, β, z and δ
      • 4.2.2 Critical Exponents for the Period Doubling Bifurcatio
    • 4.3 Extensions to Other Mapping
      • 4.3.1 Hassell Mapping
      • 4.3.2 Maynard Mappin
    • 4.4 Summar
    • 4.5 Exercise
  • 5 Introduction to Two Dimensional Mappings
    • 5.1 Linear Mapping
    • 5.2 Nonlinear Mapping
    • 5.3 Applications of Two Dimensional Mapping
      • 5.3.1 Hénon Ma
      • 5.3.2 Lyapunov Exponent
      • 5.3.3 IkedaMap
    • 5.4 Summar
    • 5.5 Exercise
  • 6 A Fermi Accelerator Mode
    • 6.1 Fermi-Ulam Model
      • 6.1.1 Jacobian Matrix for the Indirect Collision
      • 6.1.2 Jacobian Matrix for the Direct Collision
      • 6.1.3 Fixed Point
      • 6.1.4 Phase Spac
      • 6.1.5 Phase Space Measure Preservatio
    • 6.2 A Simplified Version of the Fermi-Ulam Model
    • 6.3 Scaling Properties for the Chaotic Se
    • 6.4 Localization of the First Invariant Spanning Curv
    • 6.5 The Regime of Growt
    • 6.6 Summar
    • 6.7 Exercise
  • 7 Dissipation in the Fermi-Ulam Model
    • 7.1 Dissipation via Inelastic Collision
      • 7.1.1 Jacobian Matrix for the Direct Collision
      • 7.1.2 Jacobian Matrix for the Indirect Collision
      • 7.1.3 The Phase Space
      • 7.1.4 Fixed Point
      • 7.1.5 Construction of theManifolds
      • 7.1.6 Transient and Manifold Crossings Determinatio
      • 7.1.7 Determining the Exponent δ from the Eigenvalues of the Saddle Poin
    • 7.2 Dissipation by Drag Force
      • 7.2.1 Drag Force of the Type F = −˜η
      • 7.2.2 Drag Force of the Type F = ±˜η
      • 7.2.3 Drag Force of the Type F = −˜ηv
    • 7.3 Summar
    • 7.4 Exercise
  • 8 Dynamical Properties for a Bouncer Model
    • 8.1 The Model
    • 8.2 Complete Version of the Bouncer Model
      • 8.2.1 Successive Collision
      • 8.2.2 Indirect Collision
      • 8.2.3 Jacobian Matrix
      • 8.2.4 The Phase Space
    • 8.3 A Simplified Version of the Bouncer Mode
    • 8.4 Numerical Investigation on the Simplified Versio
    • 8.5 Approximation of Continuum Tim
    • 8.6 Summar
    • 8.7 Exercise
  • 9 Localization of Invariant Spanning Curves
    • 9.1 The Standard Mappin
    • 9.2 Localization of the Curves
    • 9.3 Rescale in the Phase Spac
    • 9.4 Summar
    • 9.5 Exercise
  • 10 Chaotic Diffusion in Non-Dissipative Mapping
    • 10.1 A Family of Discrete Mappings
    • 10.2 Dynamical Properties for the Chaotic Sea:A Phenomenological Description
    • 10.3 A Semi Phenomenological Approac
    • 10.4 Determination of the Probability via the Solution of the Diffusion Equation
    • 10.5 Summar
    • 10.6 Exercise
  • 11 Scaling on a Dissipative Standard Mapping
    • 11.1 The Model
    • 11.2 A Solution for the Diffusion Equatio
    • 11.3 Specific Limit
    • 11.4 Summar
    • 11.5 Exercise
  • 12 Introduction to Billiard Dynamic
    • 12.1 The Billiard
      • 12.1.1 The Circle Billiar
      • 12.1.2 The Elliptical Billiar
      • 12.1.3 The Oval Billiard
    • 12.2 Summar
    • 12.3 Exercise
  • 13 Time Dependent Billiard
    • 13.1 The Billiard
      • 13.1.1 The LRA Conjectur
    • 13.2 The Time Dependent Elliptical Billiard
    • 13.3 The Oval Billiar
    • 13.4 Summar
    • 13.5 Exercise
  • 14 Suppression of Fermi Acceleration in the Oval Billiar
    • 14.1 The Model and the Mappin
    • 14.2 Results for the Case of F ∝ −V
    • 14.3 Results for the Case of F ∝ ±V2
    • 14.4 Results for the Case of F ∝ −Vδ
    • 14.5 Summar
    • 14.6 Exercise
  • 15 A Thermodynamic Model for Time Dependent Billiards
    • 15.1 Motivation
    • 15.2 Heat Transference
    • 15.3 The Billiard Formalis
      • 15.3.1 Stationary Estate
      • 15.3.2 Dynamical Regim
      • 15.3.3 Numerical Simulations
      • 15.3.4 Average Velocity over n
      • 15.3.5 Critical Exponent
      • 15.3.6 Distribution of Velocitie
    • 15.4 Connection Between the Two Formalis
    • 15.5 Summar
    • 15.6 Exercise
  • Appendix A: Expressions for the Coefficients
  • Appendix B: Change of Referential Frame
  • Appendix C: Solution of the Diffusion Equation
  • Appendix D: Heat Flow Equatio
  • Appendix E: Connection Between t and n in a Time Dependent Oval Billiar
  • Appendix F: Solution of the Integral to Obtain the Relation Between n and t in the Time Dependent Oval Billiard
  • Bibliograph

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