实用符号动力学与混沌
正版保障 假一赔十 可开发票
￥ 63.84 6.7折 ￥ 95 全新
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广东广州
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作者郝柏林，郑伟谋编著
出版社北京大学出版社
ISBN9787301247563
出版时间2013-02
装帧平装
开本16开
定价95元
货号8354754
上书时间2024-12-22
商品详情
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作者简介
郝柏林，1934年6月生。毕业于苏联哈尔科夫国立大学物理数学系。中国科学院院士、第三世界科学院院士，中国科学院理论物理研究所研究员，复旦大学理论生命科学研究中心教授。从事理论物理、统计物理、计算物理、非线性科学和理论生命科学研究，发表科学论文140余篇，已出版中英文书14种。获国家自然科学二等奖(2次)、全国很好科技图书奖二等奖、全国很好科普作品一等奖、中国科学院自然科学奖一等奖(2次)、美国ISI的1981～1998年度经典引文奖、何梁何利基金科学与技术进步奖物理学奖。
郑伟谋，中国科学院理论物理研究所研究员。主要从事量子力学、统计物理、非线性动力学和生物信息学的研究。
目录
Preface for the Second Edition
Preface
1 Introduction
1.1 Dynamical Systems
1.1.1 Phase Space and Orbits
1.1.2 Parameters and Bifurcation of Dynamical Behavior
1.1.3 Examples of Dynamical Systems
1.2 Symbolic Dynamics as Coarse-Grained Description of Dynamics--
1.2.1 Fine-Grained and Coarse-Grained Descriptions
1.2.2 Symbolic Dynamics as the Simplest Dynamics
1.3 Abstract versus Applied Symbolic Dynamics
1.3.1 Abstract Symbolic Dynamics
1.3.2 Applied Symbolic Dynamics
1.4 Literature on Symbolic Dynamics
2 Symbolic Dynamics of Unimodal Maps
2.1 Symbolic Sequences in Unimodal Maps
2.1.1 Numerical Orbit and Symbolic Sequence
2.1.2 Symbolic Sequence and Functional Composition
2.1.3 The Word-Lifting Technique
2.2 The Quadratic Map
2.2.1 An Over-Simplified Population Model
2.2.2 Bifurcation Diagram of the Quadratic Map
2.2.3 Dark Lines in the Bifurcation Diagram
2.3 Ordering of Symbolic Sequences and the Admissibility Condition
2.3.1 Property of Monotone Fhnctions
2.3.2 The Ordering Rule
2.3.3 Dynamical Invariant Range and Kneading Sequence
2.3.4 The Admissibility Condition
2.4 The Periodic Window Theorem
2.4.1 The Periodic Window Theorem
2.4.2 Construction of Median Words
2.4.3 The MSS Table of Kneading Sequences
2.4.4 Nomenclature of Unstable Periodic Orbits
2.5 Composition Rules
2.5.1 The *-Composition
2.5.2 Generalized Composition Rule
2.5.3 Proof of the Generalized Composition Rule
2.5.4 Applications of the Generalized Composition Rule
2.5.5 Further Remarks on Composition Rules
2.6 Coarse-Grained Chaos
2.6.1 Chaos in the Surjective Unimodal Map
2.6.2 Chaos in pλ∞ Maps
2.7 Topological Entropy
2.8 Piecewise Linear Maps and Metric Representation of Symbolic Sequences
2.8.1 The Tent Map and Shift Map
……
3 Maps with Multiple Critical Points
4 Symbolic Dynamics of Circle Maps
5 Symbolic Dynamics of Two-Dimensional Maps
6 Application to Ordinary Differential Equations
7 Counting the Number of Periodic Orbits
8 Symbolic Dynamics and Grammatical Complexity
9 Symbolic Dynamics and Knot Theory
10 Appendix
References
Index
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