Dynamics in one complex variable / by John Milnor.

Format:

Book

Author/Creator:

Milnor, John W. (John Willard), 1931-

Series:

Annals of mathematics studies ; no. 160.

Annals of mathematics studies ; no. 160

Language:

English

Subjects (All):

Functions of complex variables.

Holomorphic mappings.

Riemann surfaces.

Physical Description:

1 online resource (313 p.)

Edition:

3rd ed.

Place of Publication:

Princeton, N.J. : Princeton University Press, 2006.

Language Note:

English

Summary:

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 Lattés map has been made more inclusive, and the écalle-Voronin theory of parabolic points is described. The résidu itératif 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.

Contents:

Frontmatter

Table Of Contents

List of Figures

Preface to the Third Edition

Chronological Table

Riemann Surfaces

Iterated Holomorphic Maps

Local Fixed Point Theory

Periodic Points: Global Theory

Structure of the Fatou Set

Using the Fatou Set to Study the Julia Set

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

Notes:

Description based upon print version of record.

Includes bibliographical references (p. 277-291) and index.

ISBN:

9786613001481

9781283001489

1283001489

9781400835539

1400835534

OCLC:

705539236