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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
版面字数：
460千字
开本：
特殊
装帧形式：
精装
版次：
1
最新版次
印刷时间：
2022年
ISBN：
978-7-04-057212-4
物料号：
57212-00
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
  • 目录
    • 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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