Complex Dynamics and Renormalization (AM-135) (Annals of Mathematics Studies, 135) - Softcover

McMullen, Curtis T.

Softcover

ISBN 10: 0691029814 ISBN 13: 9780691029818

Verlag: Princeton University Press, 1994

Inhaltsangabe

Book by McMullen Curtis T

Über diesen Titel

Críticas

Curtis T. McMullen, Winner of the 1998 Fields Medal, International Congress of Mathematicians "This book presents a great many ideas very clearly and should prove to be a valuable addition to the complex dynamics literature."--Mathematical Reviews

Reseña del editor

Addressing researchers and graduate students in the active meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and a rapid introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c. As discovered by Feigenbaum, such a mapping exhibits a repetition of form at infinitely many scales. Drawing on universal estimates in hyperbolic geometry, this work gives an analysis of the limiting forms that can occur and develops a rigidity criterion for the polynomial f. This criterion supports general conjectures about the behavior of rational maps and the structure of the Mandelbrot set. The course of the main argument entails many facets of modern complex dynamics. Included are foundational results in geometric function theory, quasiconformal mappings, and hyperbolic geometry. Most of the tools are discussed in the setting of general polynomials and rational maps.

Details zur Ausgabe

• Verlag: Princeton University Press
• Erscheinungsdatum: 1994
• ISBN 10: 0691029814
• ISBN 13: 9780691029818
• Einband: Tapa blanda
• Sprache: Englisch
• Anzahl der Seiten: 228