Introduction to the Modern Theory of Dynamical Systems: Low-dimensional phenomena
Introduction to the Modern Theory of Dynamical Systems: Low-dimensional phenomena
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DOI：
10.1017/cbo9780511809187
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发表时间：
1995-04
期刊：
影响因子：
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通讯作者：
A. Katok;B. Hasselblatt
中科院分区：
文献类型：
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作者：
A. Katok;B. Hasselblatt
第一部分.示例和基本概念介绍1.第一个例子2.等价性、分类和不变量3。渐近不变量的原理类4.轨道的统计行为和遍历理论的介绍5.平滑不变测度和更多示例第二部分。局部分析和轨道增长6.局部双曲理论及其应用7. 8.第八章.由拓扑结构引起的轨道增长9.动力学的变分问题第三部分。10.第二次世界大战简介：什么是低维动力学11. 12.第12章大结局13.第十三章14.第十四章表面上的流动和相关的动力系统15. 16.第16章.区间光滑映射第四部分. 17.第一次约会18.第十八章.双曲集的拓扑性质19. 20.第20章大结局平衡态和光滑不变测度第五部分Sopplement和附录21。具有非一致双曲行为的动力系统Anatole Katok和列奥纳多门多萨。
Part I. Examples and Fundamental Concepts Introduction 1. First examples 2. Equivalence, classification, and invariants 3. Principle classes of asymptotic invariants 4. Statistical behavior of the orbits and introduction to ergodic theory 5. Smooth invariant measures and more examples Part II. Local Analysis and Orbit Growth 6. Local hyperbolic theory and its applications 7. Transversality and genericity 8. Orbit growth arising from topology 9. Variational aspects of dynamics Part III. Low-Dimensional Phenomena 10. Introduction: What is low dimensional dynamics 11. Homeomorphisms of the circle 12. Circle diffeomorphisms 13. Twist maps 14. Flows on surfaces and related dynamical systems 15. Continuous maps of the interval 16. Smooth maps of the interval Part IV. Hyperbolic Dynamical Systems 17. Survey of examples 18. Topological properties of hyperbolic sets 19. Metric structure of hyperbolic sets 20. Equilibrium states and smooth invariant measures Part V. Sopplement and Appendix 21. Dynamical systems with nonuniformly hyperbolic behavior Anatole Katok and Leonardo Mendoza.