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- catalog abstract "This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. The conceptual kernel is a self-contained abstract counterpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated in the complex plane. It is used to give rigorous proofs of some well-known and some partially new statements on the structure of the Mandelbrot set. The text is intended for graduate students and researchers. Some elementary knowledge in topology and in functions of one complex variable is assumed.".
- catalog contributor b11693379.
- catalog created "2000.".
- catalog date "2000".
- catalog date "2000.".
- catalog dateCopyrighted "2000.".
- catalog description "1. Introduction: Quadratic iteration and Julia equivalences. The Mandelbrot set -- 2. Abstract Julia sets: Symbolic dynamics of the angle-doubling map. Invariant laminations. Julia equivalences -- 3. The Abstract Mandelbrot set: The Abstract Mandelbrot set - an atlas of Abstract Julia sets. The ordered Abstract Mandelbrot set. Renormalization. Correspondence and Translation Principles -- 4. Abstract and concrete theory: Quadratic iteration. Miscellaneous. Appendix: Invariant and completely invariant factors. Simple statements. Shift-invariant factors. Further interesting examples.".
- catalog description "Includes bibliographical references and index.".
- catalog description "This book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. The conceptual kernel is a self-contained abstract counterpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated in the complex plane. It is used to give rigorous proofs of some well-known and some partially new statements on the structure of the Mandelbrot set. The text is intended for graduate students and researchers. Some elementary knowledge in topology and in functions of one complex variable is assumed.".
- catalog extent "x, 205 p. :".
- catalog identifier "3540674349 (softcover : alk. paper)".
- catalog isPartOf "Lecture notes in mathematics (Springer-Verlag) ; 1732.".
- catalog isPartOf "Lecture notes in mathematics, 0075-8434 ; 1732".
- catalog issued "2000".
- catalog issued "2000.".
- catalog language "eng".
- catalog publisher "New York : Springer,".
- catalog subject "+ QA614.85".
- catalog subject "510 s 514/.74 21".
- catalog subject "Analytic functions.".
- catalog subject "Differential equations, partial.".
- catalog subject "Functions of complex variables.".
- catalog subject "Mathematics.".
- catalog subject "Symbolic dynamics.".
- catalog subject "Topological dynamics.".
- catalog subject "Topology.".
- catalog tableOfContents "1. Introduction: Quadratic iteration and Julia equivalences. The Mandelbrot set -- 2. Abstract Julia sets: Symbolic dynamics of the angle-doubling map. Invariant laminations. Julia equivalences -- 3. The Abstract Mandelbrot set: The Abstract Mandelbrot set - an atlas of Abstract Julia sets. The ordered Abstract Mandelbrot set. Renormalization. Correspondence and Translation Principles -- 4. Abstract and concrete theory: Quadratic iteration. Miscellaneous. Appendix: Invariant and completely invariant factors. Simple statements. Shift-invariant factors. Further interesting examples.".
- catalog title "Invariant factors, Julia equivalences, and the (abstract) Mandelbrot set / Karsten Keller.".
- catalog type "text".