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Dynamics in one complex variable Third Edition by John Willard Milnor ISBN 978-0691124889 0691124884

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Author(s): John Willard Milnor
ISBN(s): 9780691124889, 0691124884
Edition: 3
File Details: PDF, 4.04 MB
Year: 2006
Language: english
SKU: EB-2126130 Category: Tag:

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ISBN 10:   0691124884

ISBN 13: 978-0691124889

Author: John Willard Milnor 

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.

Table of contents: 

  1. FrontMatter

  2. Table Of Contents

  3. List of Figures

  4. Preface to the Third Edition

  5. Chronological Table

  6. Riemann Surfaces

  7. Iterated Holomorphic Maps

  8. Local Fixed Point Theory

  9. Periodic Points: Global Theory

  10. Structure of the Fatou Set

  11. Using the Fatou Set to Study the Julia Set

  12. Appendix A. Theorems from Classical Analysis

  13. Appendix B. Length-Area-Modulus Inequalities

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

  15. Appendix D. Two or More Complex Variables

  16. Appendix E. Branched Coverings and Orbifolds

  17. Appendix F. No Wandering Fatou Components

  18. Appendix G. Parameter Spaces

  19. Appendix H. Computer Graphics and Effective Computation

  20. References

  21. Index

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