Milnor Dynamics in One Complex Variable

Third Edition
Third Auflage
ISBN: 978-1-4008-3553-9
Verlag: De Gruyter
Format: EPUB
Kopierschutz: Adobe DRM (»Systemvoraussetzungen)

E-Book, Englisch, 320 Seiten

Reihe: Annals of Mathematics Studies

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.

Autoren/Hrsg.

Milnor, John

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein

Inhaltsverzeichnis

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

Über Autor(innen)

John Milnor is Professor of Mathematics and Co-Director of the Institute for Mathematical Sciences at SUNY, Stony Brook. He is the author of Topology from the Differential Viewpoint, Singular Points of Complex Hypersurfaces, Morse Theory, Introduction to Algebraic K-Theory, Characteristic Classes (with James Stasheff), and Lectures on the H-Cobordism Theorem (Princeton).