Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set [[electronic resource] /] / by Karsten Keller
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| Autore: |
Keller Karsten
|
| Titolo: |
Invariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set [[electronic resource] /] / by Karsten Keller
|
| Pubblicazione: | Berlin, Heidelberg : , : Springer Berlin Heidelberg : , : Imprint : Springer, , 2000 |
| Edizione: | 1st ed. 2000. |
| Descrizione fisica: | 1 online resource (XII, 208 p.) |
| Disciplina: | 514.74 |
| Soggetto topico: | Partial differential equations |
| Topology | |
| Partial Differential Equations | |
| Classificazione: | 37B10 |
| 54H20 | |
| 30D05 | |
| Note generali: | Bibliographic Level Mode of Issuance: Monograph |
| Nota di bibliografia: | Includes bibliographical references and index. |
| Nota di contenuto: | 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. |
| Sommario/riassunto: | 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. |
| Titolo autorizzato: | Invariant factors, Julia equivalences and the (abstract) Mandelbrot set |
| ISBN: | 3-540-45589-2 |
| Formato: | Materiale a stampa  |
| Livello bibliografico | Monografia |
| Lingua di pubblicazione: | Inglese |
| Record Nr.: | 9910146314503321 |
| Lo trovi qui: | Univ. Federico II |
| Opac: | Controlla la disponibilità qui |
Serie:
Lecture Notes in Mathematics, . 0075-8434 ; ; 1732