单复变量动力系统 : 第3版

ListofFiguresPreface to the Third EditionChronological Table Riemann Surfaces1. Simply Connected Surfaces2. Universal Coverings and the Poincare Metric3. Normal Families： Montel's TheoremIterated Holomorphic Maps4. Fatou and Julia： Dynamics on the Riemann Sphere5. Dynamics on Hyperbolic Surfaces 6. Dynamics on Euclidean Surfaces7. Smooth Julia Sets Local Fixed Point Theory8. Geometrically Attracting or Repelling Fixed Points9. Bottcher's Theorem and Polynomial Dynamics10. Parabolic Fixed Points： The Leau-Fatou Flower11. Cremer Points and Siegel DisksPeriodic Points： Global Theory12. The Holomorphic Fixed Point Formula 13. Most Periodic Orbits Repel 14. Repelling Cycles Are Dense in JStructure of the Fatou Set15. Herman Rings16. The Sullivan Classification of Fatou ComponentsUsing the Fatou Set to Study the Julia Set17. Prime Ends and Local Connectivity18. Polynomial Dynamics： External Rays19. Hyperbolic and Subhyperbolic Maps Appendix A. Theorems from Classical AnalysisAppendix B. Length-Area-Modulus Inequalities Appendix C. Rotations， Continued Fractions， and Rational ApproximationAppendix D. Two or More Complex VariablesAppendix E. Branched Coverings and Orbifolds Appendix F. No Wandering Fatou Components Appendix G. Parameter SpacesAppendix H. Computer Graphics and Effective ComputationReferences Index

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.