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单复变动力系统 第3版 英文影印版 [JohnMilnor 著] 2013年版
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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
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