单复变动力系统 第3版 英文影印版 作者：JohnMilnor 著 出版时间：2013年版 内容简介 This book studies the dynamics of iterated holomorphic mappings from a Riemann surface to itself，concentrating on the classical case of rational . maps of the Riemann sphere. It is based on introductory lectures given at Stony Brook during the fall term of 1989-90 and in later years.I am grateful to the audiences for a great deal of constructive criticism and to Bodil Branner， Adrien Douady， John Hubbard， and Mitsuhiro Shishikura， who taught me most of what I know in this field. Also， I want to thank a number of individuals for their extremely helpful criticisms and suggestions， especially Adam Epstein， Rodrigo Perez， Alfredo Poirier， Lasse Rempe， and Saeed Zakeri. Araceli Bonifant has been particularly helpful in the preparation of this third edition. 目录 ListofFigures Preface to the Third Edition Chronological Table Riemann Surfaces 1. Simply Connected Surfaces 2. Universal Coverings and the Poincare Metric 3. Normal Families: Montel's Theorem Iterated Holomorphic Maps 4. Fatou and Julia: Dynamics on the Riemann 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. Bottcher's Theorem and Polynomial Dynamics 10. Parabolic Fixed Points: The Leau-Fatou Flower 11. Cremer Points and Siegel Disks 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 Fatou 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. Theorems from Classical Analysis Appendix B. Length-Area-Modulus Inequalities Appendix C. Rotations, Continued Fractions, and Rational Approximation Appendix D. Two or More Complex Variables Appendix E. Branched Coverings and Orbifolds Appendix F. No Wandering Fatou Components Appendix G. Parameter Spaces Appendix H. Computer Graphics and Effective Computation References Index
