03504nam 22006735 450 991014631450332120220329163143.03-540-45589-210.1007/BFb0103999(CKB)1000000000437282(SSID)ssj0000324167(PQKBManifestationID)12080840(PQKBTitleCode)TC0000324167(PQKBWorkID)10304197(PQKB)11127623(DE-He213)978-3-540-45589-9(MiAaPQ)EBC6286512(MiAaPQ)EBC5579094(Au-PeEL)EBL5579094(OCoLC)1066186681(PPN)155189077(EXLCZ)99100000000043728220121227d2000 u| 0engurnn#008mamaatxtccrInvariant Factors, Julia Equivalences and the (Abstract) Mandelbrot Set /by Karsten Keller1st ed. 2000.Berlin, Heidelberg :Springer Berlin Heidelberg :Imprint: Springer,2000.1 online resource (XII, 208 p.)Lecture Notes in Mathematics,0075-8434 ;1732Bibliographic Level Mode of Issuance: Monograph3-540-67434-9 Includes bibliographical references and index.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.Lecture Notes in Mathematics,0075-8434 ;1732Partial differential equationsTopologyPartial Differential Equationshttps://scigraph.springernature.com/ontologies/product-market-codes/M12155Topologyhttps://scigraph.springernature.com/ontologies/product-market-codes/M28000Partial differential equations.Topology.Partial Differential Equations.Topology.514.7437B10msc54H20msc30D05mscKeller Karstenauthttp://id.loc.gov/vocabulary/relators/aut62627MiAaPQMiAaPQMiAaPQBOOK9910146314503321Invariant factors, Julia equivalences and the (abstract) Mandelbrot set78789UNINA