Complex Dynamics and Renormalization (AM-135), Volume 135

Contents\n1 Introduction\n	1.1 Complex dynamics\n	1.2 Central conjectures\n	1.3 Summary of contents\n2 Background in conformal geometry\n	2.1 The modulus of annulus\n	2.2 The hyperbolic metric\n	2.3 Metric aspects of annuli\n	2.4 Univalent maps\n	2.5 Normal families\n	2.6 Quasiconformal maps\n	2.7 Measurable sets\n	2.8 Absolute area zero\n	2.9 The collar theorem\n	2.10 The complex shortest interval argument\n	2.11 Controlling holomorphic contraction\n3 Dynamics of rational maps\n	3.1 The Julia and Fatou sets\n	3.2 Expansion\n	3.3 Ergodicity\n	3.4 Hyperbolicity\n	3.5 Invariant line fields and complex tori\n4 Holomorphic motions and the Mandelbrot set\n	4.1 Stability of rational maps\n	4.2 The Mandelbrot set\n5 Compactness in holomorphic dynamics\n	5.1 Convergence of Riemann mappings\n	5.2 Proper maps\n	5.3 Polynomial-like maps\n	5.4 Intersecting polynomial-like maps\n	5.5 Polynomial-like maps inside proper maps\n	5.6 Univalent line fields\n6 Polynomials and external rays\n	6.1 Accessibility\n	6.2 Polynomials\n	6.3 Eventual surjectivity\n	6.4 Laminations\n7 Renormalization\n	7.1 Quadratic polynomials\n	7.2 Small Julia sets meeting at periodic points\n	7.3 Simple renormalization\n	7.4 Examples\n8 Puzzles and infinite renormalization\n	8.1 Infinite renormalization\n	8.2 The Yoccoz jigsaw puzzle\n	8.3 Infinite simple renormalization\n	8.4 Measure and local connectivity\n	8.5 Laminations and tableaux\n9 Robustness\n	9.1 Simple loops around the postcritical set\n	9.2 Area of the postcritical set\n10 Limits of renormalization\n	10.1 Unbranched renormalization\n	10.2 Polynomial-like limits of renormalization\n	10.3 Proper limits of renormalization\n	10.4 Extracting a univalent line field\n11 Real quadratic polynomials\n	11.1 Intervals and gaps\n	11.2 Real robustness\n	11.3 Corollaries and generalizations\nA Orbifolds\n	A.1 Smooth and complex orbifolds\n	A.2 Coverings and uniformization\n	A.3 The orbifold of a rational map\nB A closing lemma for rational maps\n	B.1 Quotients of branched coverings\n	B.2 Critically finite rational maps\n	B.3 Siegel disks, Herman rings and curve systems\n	B.4 Rational quotients\n	B.5 Quotients and renormalization\nBibliography\nIndex