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＜電子ブック＞
Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set / by Karsten Keller
(Lecture Notes in Mathematics. ISSN:16179692 ; 1732)

版	1st ed. 2000.
出版者	(Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer)
出版年	2000
本文言語	英語
大きさ	XII, 208 p : online resource
著者標目	*Keller, Karsten author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Topology FREE:Differential Equations FREE:Topology
一般注記	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 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 HTTP:URL=https://doi.org/10.1007/BFb0103999

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