Complex Dynamics and Renormalization - Rilegato

McMullen, Curtis T.

Rilegato

ISBN 10: 0691029822 ISBN 13: 9780691029825

Casa editrice: Princeton Univ Pr, 1995

Riassunto

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 polynomialf(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.

Su questo libro

Recensione

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

Contenuti

• Background in conformal geometry
• Dynamics of rational maps
• Holomorphic motions and the Mandelbrot set
• Compactness in holomorphic dynamics
• Polynomials and external rays
• Renormalization
• Puzzles and infinite renormalization
• Robustness
• Limits of renormalization
• Real quadratic polynomials

Dettagli dell'edizione

• Editore: Princeton Univ Pr
• Data di pubblicazione: 1995
• Lingua: Inglese
• ISBN 10: 0691029822
• ISBN 13: 9780691029825
• Rilegatura: Copertina rigida
• Numero di pagine: 214
• Contatto del produttore: non disponibile
• Persona responsabile: non disponibile