Dynamics in One Complex Variable

Third Edition

By: John Milnor

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Paperback | 22 January 2006 | Edition Number 3

At a Glance

Paperback
320 Pages

Edition Type
Revised

Dimensions(cm)
25.4 x 17.7 x 1.7

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This volume 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. This subject is large and rapidly growing. These lectures are intended to introduce some key ideas in the field, and to form a basis for further study. The reader is assumed to be familiar with the rudiments of complex variable theory and of two-dimensional differential geometry, as well as some basic topics from topology. This third edition contains a number of minor additions and improvements: A historical survey has been added, the definition of Lattes map has been made more inclusive, and the ecalle-Voronin theory of parabolic points is described. The residu iteratif is studied, and the material on two complex variables has been expanded. Recent results on effective computability have been added, and the references have been expanded and updated.

Written in his usual brilliant style, the author makes difficult mathematics look easy. This book is a very accessible source for much of what has been accomplished in the field.

Industry Reviews

"John Milnor's book provides a solid foundation and the kind of bird's eye view that perhaps only a mathematician of his caliber can offer."--William J. Satzer, MAA Reviews

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You Can Find This Book In

Non-Fiction Mathematics Calculus & Mathematical Analysis Complex Analysis

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Non-Fiction Mathematics Calculus & Mathematical Analysis Complex Analysis

List of Figures	p. vi
Preface to the Third Edition	p. vii
Chronological Table	p. viii
Riemann Surfaces
Simply Connected Surfaces	p. 1
Universal Coverings and the Poincare Metric	p. 13
Normal Families: Montel's Theorem	p. 30
Iterated Holomorphic Maps
Fatou and Julia: Dynamics on the Riemann Sphere	p. 39
Dynamics on Hyperbolic Surfaces	p. 56
Dynamics on Euclidean Surfaces	p. 65
Smooth Julia Sets	p. 69
Local Fixed Point Theory
Geometrically Attracting or Repelling Fixed Points	p. 76
Bottcher's Theorem and Polynomial Dynamics	p. 90
Parabolic Fixed Points: The Leau-Fatou Flower	p. 104
Cremer Points and Siegel Disks	p. 125
Periodic Points: Global Theory
The Holomorphic Fixed Point Formula	p. 142
Most Periodic Orbits Repel	p. 153
Repelling Cycles Are Dense in J	p. 156
Structure of the Fatou Set
Herman Rings	p. 161
The Sullivan Classification of Fatou Components	p. 167
Using the Fatou Set to Study the Julia Set
Prime Ends and Local Connectivity	p. 174
Polynomial Dynamics: External Rays	p. 188
Hyperbolic and Subhyperbolic Maps	p. 205
Theorems from Classical Analysis	p. 219
Length-Area-Modulus Inequalities	p. 226
Rotations, Continued Fractions, and Rational Approximation	p. 234
Two or More Complex Variables	p. 246
Branched Coverings and Orbifolds	p. 254
No Wandering Fatou Components	p. 259
Parameter Spaces	p. 266
Computer Graphics and Effective Computation	p. 271
References	p. 277
Index	p. 293
Table of Contents provided by Ingram. All Rights Reserved.

Dynamics in One Complex Variable

Third Edition

At a Glance

Paperback

Industry Reviews

Shipping

How to return your order

Defective items

You Can Find This Book In

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