03795nam 22007095 450 991029999170332120200630093546.03-319-11707-610.1007/978-3-319-11707-2(CKB)3710000000271804(EBL)1966899(SSID)ssj0001386491(PQKBManifestationID)11826482(PQKBTitleCode)TC0001386491(PQKBWorkID)11374504(PQKB)10272660(MiAaPQ)EBC1966899(DE-He213)978-3-319-11707-2(PPN)183091353(EXLCZ)99371000000027180420141101d2014 u| 0engur|n|---|||||txtccrFixed Point of the Parabolic Renormalization Operator[electronic resource] /by Oscar E. Lanford III, Michael Yampolsky1st ed. 2014.Cham :Springer International Publishing :Imprint: Springer,2014.1 online resource (119 p.)SpringerBriefs in Mathematics,2191-8198Description based upon print version of record.3-319-11706-8 Includes bibliographical references and index.1 Introduction -- 2 Local dynamics of a parabolic germ -- 3 Global theory -- 4 Numerical results -- 5 For dessert: several amusing examples -- Index.This monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point.   Inside, readers will find a detailed introduction into the theory of parabolic bifurcation,  Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization.   The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishing to explore one of the frontiers of modern complex dynamics.SpringerBriefs in Mathematics,2191-8198DynamicsErgodic theoryFunctions of complex variablesNumerical analysisDynamical Systems and Ergodic Theoryhttps://scigraph.springernature.com/ontologies/product-market-codes/M1204XFunctions of a Complex Variablehttps://scigraph.springernature.com/ontologies/product-market-codes/M12074Numerical Analysishttps://scigraph.springernature.com/ontologies/product-market-codes/M14050Dynamics.Ergodic theory.Functions of complex variables.Numerical analysis.Dynamical Systems and Ergodic Theory.Functions of a Complex Variable.Numerical Analysis.510515.39515.48515.9518Lanford III Oscar Eauthttp://id.loc.gov/vocabulary/relators/aut1060590Yampolsky Michaelauthttp://id.loc.gov/vocabulary/relators/autBOOK9910299991703321Fixed Point of the Parabolic Renormalization Operator2514375UNINA