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