单复变动力系统 第3版 英文PDF电子书下载

Riemann Surfaces 1

1．Simply Connected Surfaces 1

2．Universal Coverings and the PoincaréMetric 13

3．Normal Families：Montel's Theorem 30

Iterated Holomorphic Maps 39

4．Fatou and Julia：Dynamics on the Riemann Sphere 39

5．Dynamics on Hyperbolic Surfaces 56

6．Dynamics on Euclidean Surfaces 65

7．Smooth Julia Sets 69

Local Fixed Point Theory 76

8．Geometrically Attracting or Repelling Fixed Points 76

9．B？ttcher's Theorem and Polynomial Dynamics 90

10．Parabolic Fixed Points：The Leau-Fatou Flower 104

11．Cremer Points and Siegel Disks 125

Periodic Points：Global Theory 142

12．The Holomorphic Fixed Point Formula 142

13．Most Periodic Orbits Repel 153

14．Repelling Cycles Are Dense in J 156

Structure of the Fatou Set 161

15．Herman Rings 161

16．The Sullivan Classification of Fatou Components 167

Using the Fatou Set to Study the Julia Set 174

17．Prime Ends and Local Connectivity 174

18．Polynomial Dynamics：External Rays 188

19．Hyperbolic and Subhyperbolic Maps 205

Appendix A．Theorems from Classical Analysis 219

Appendix B．Length-Area-Modulus Inequalities 226

Appendix C．Rotations,Continued Fractions,and Rational Approximation 234

Appendix D．Two or More Complex Variables 246

Appendix E．Branched Coverings and Orbifolds 254

Appendix F．No Wandering Fatou Components 259

Appendix G．Parameter Spaces 266

Appendix H．Computer Graphics and Effective Computation 271

References 277

Index 293