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