米尔诺著的《单复变动力系统(第3版)》旨在研究从黎曼曲面到黎曼曲面迭代正则映射的动力学理论,专注于黎曼球面经典案例。该科目内容庞大,发展迅速,本书将引进这个领域的核心理念,并且形成更进一步研究的基础。本书假定读者有一定的复变量、二维微分几何和拓扑知识。这是第三版,在原来版本的基础上做了小的改动和改进,包括一个小的历史回顾、Latts映射定义、抛物点calle-Voronin理论、扩充了二复变量的知识、增加了有效计算性的最新结果,参考资料做了扩展和更新。
List of Figures
Preface tothe Third Edition
Chronological Table
Riemann Surfaces
1. Simply Connected Surfaces
2. Universal Coverings andthePoincardMetric
3. Normal Families:Moutel's Theorem
Iterated Holomorphlc Maps
4. Fatou and Julia:Dynamics ontheRiemann Sphere
5. Dynamics on Hyperbolic Surfaces
6. Dynamics on Euclidean Surfaces
7. Smooth Julia Sets
Local Fixed Point Theory
8. Geometrically Attracting or Repelling Fixed Points
9. B6ttcher's Theorem and Polynomial Dynamics
10. ParabolicFixed Points:The Lean-Faton Flower
11. Cremer Points and SiegelDisks,
Periodic Points:Global Theory
12. The Holomorphic Fixed Point Formula
13. Most Periodic Orbits Repel
14. Repelling Cycles Are Dense in J
Structure of the Fatou Set
15. Herman Rings
16. The Sullivan Classification of FatOH Components
Using the Fatou Set to Study the Julia Set
17. Prime Ends and Local Connectivity
18. Polynomial Dynamics:External Rays
19. Hyperbolic and Subhyperbolic Maps
Appendix A.Theoremsfrom ClassicalAnalysis
Appendix B.Length-Area-Modulus Inequalities
Appendix C.Rotations,Continued Fractions,and Rational Approximation
Appendix D.Two or More Complex Variables
Appendix E.BranchedCoverings and Orbifolds
Appendix F.NoWandering Fatou Components
Appendix G.Parameter Spaces
Appendix H.Computer Graphics and Effective Computation
References
Index