Complex Dynamics and Renormalization (AM-135), Volume 135
Seiten
1994
Princeton University Press (Verlag)
978-0-691-02981-8 (ISBN)
Princeton University Press (Verlag)
978-0-691-02981-8 (ISBN)
Addressing researchers and graduate students in the meeting ground of analysis, geometry, and dynamics, this book presents a study of renormalization of quadratic polynomials and an introduction to techniques in complex dynamics. Its central concern is the structure of an infinitely renormalizable quadratic polynomial f(z) = z2 + c.
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.
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.
Curtis T. McMullen is Professor of Mathematics at the University of California, Berkeley.
* 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
| Erscheint lt. Verlag | 19.12.1994 |
|---|---|
| Reihe/Serie | Annals of Mathematics Studies |
| Zusatzinfo | 31 line drawings |
| Verlagsort | New Jersey |
| Sprache | englisch |
| Maße | 197 x 254 mm |
| Gewicht | 312 g |
| Themenwelt | Mathematik / Informatik ► Mathematik ► Analysis |
| Mathematik / Informatik ► Mathematik ► Graphentheorie | |
| ISBN-10 | 0-691-02981-4 / 0691029814 |
| ISBN-13 | 978-0-691-02981-8 / 9780691029818 |
| Zustand | Neuware |
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