Dynamics in one complex variable

Author(s)

• Milnor, John Willard

Bibliographic Information

Dynamics in one complex variable

by John Milnor

（Annals of mathematics studies, no. 160）

Princeton University Press, 2006

3rd ed

• : [hbk]
• : pbk

Note

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

Description and Table of Contents

Volume

: [hbk] ISBN 9780691124872

Description

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.

Volume

: pbk ISBN 9780691124889

Description

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.

Table of Contents

*FrontMatter, pg. i*Table Of Contents, pg. v*List of Figures, pg. vi*Preface to the Third Edition, pg. vii*Chronological Table, pg. viii*Riemann Surfaces, pg. 1*Iterated Holomorphic Maps, pg. 39*Local Fixed Point Theory, pg. 76*Periodic Points: Global Theory, pg. 142*Structure of the Fatou Set, pg. 161*Using the Fatou Set to Study the Julia Set, pg. 174*Appendix A. Theorems from Classical Analysis, pg. 219*Appendix B. Length-Area-Modulus Inequalities, pg. 226*Appendix C. Rotations, Continued Fractions, and Rational Approximation, pg. 234*Appendix D. Two or More Complex Variables, pg. 246*Appendix E. Branched Coverings and Orbifolds, pg. 254*Appendix F. No Wandering Fatou Components, pg. 259*Appendix G. Parameter Spaces, pg. 266*Appendix H. Computer Graphics and Effective Computation, pg. 271*References, pg. 277*Index, pg. 293

by "Nielsen BookData"

Details

• NCID: BA75128655
• ISBN:
  • 9780691124872
  • 9780691124889
• LCCN: 2005051060
• Country Code: us
• Title Language Code: eng
• Text Language Code: eng
• Place of Publication: Princeton, N.J.
• Pages/Volumes: viii, 304 p.
• Size: 27 cm
• Classification:
  • LCC : QA331.7
  • DC22 : 515/.93
• Subject Headings:
  • LCSH : Functions of complex variables
  • LCSH : Holomorphic mappings
  • LCSH : Riemann surfaces
• Parent Bibliography ID:
  • BA00300336