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100   $a20121227d2000      u|         0
101 0 $aeng
135   $aurnn#008mamaa
181   $ctxt
182   $cc
183   $acr
200 10$aInvariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set /$fby Karsten Keller
205   $a1st ed. 2000.
210  1$aBerlin, Heidelberg :$cSpringer Berlin Heidelberg :$cImprint: Springer,$d2000.
215   $a1 online resource (XII, 208 p.)
225 1 $aLecture Notes in Mathematics,$x0075-8434 ;$v1732
300   $aBibliographic Level Mode of Issuance: Monograph
311   $a3-540-67434-9 
320   $aIncludes bibliographical references and index.
327   $a1. 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.
330   $aThis book is mainly devoted to the combinatorics of quadratic holomorphic dynamics. The conceptual kernel is a self-contained abstract counterpart of connected quadratic Julia sets which is built on Thurston's concept of a quadratic invariant lamination and on symbolic descriptions of the angle-doubling map. The theory obtained is illustrated in the complex plane. It is used to give rigorous proofs of some well-known and some partially new statements on the structure of the Mandelbrot set. The text is intended for graduate students and researchers. Some elementary knowledge in topology and in functions of one complex variable is assumed.
410  0$aLecture Notes in Mathematics,$x0075-8434 ;$v1732
606   $aDifferential equations, Partial
606   $aTopology
606   $aPartial Differential Equations$3https://scigraph.springernature.com/ontologies/product-market-codes/M12155
606   $aTopology$3https://scigraph.springernature.com/ontologies/product-market-codes/M28000
615  0$aDifferential equations, Partial.
615  0$aTopology.
615 14$aPartial Differential Equations.
615 24$aTopology.
676   $a514.74
686   $a37B10$2msc
686   $a54H20$2msc
686   $a30D05$2msc
700   $aKeller$b Karsten$4aut$4http://id.loc.gov/vocabulary/relators/aut$062627
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910146314503321
996   $aInvariant factors, Julia equivalences and the (abstract) Mandelbrot set$978789
997   $aUNINA