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010   $a3-319-11707-6
024 7 $a10.1007/978-3-319-11707-2
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100   $a20141101d2014      u|         0
101 0 $aeng
135   $aur|n|---|||||
181   $ctxt
182   $cc
183   $acr
200 10$aFixed Point of the Parabolic Renormalization Operator /$fby Oscar E. Lanford III, Michael Yampolsky
205   $a1st ed. 2014.
210  1$aCham :$cSpringer International Publishing :$cImprint: Springer,$d2014.
215   $a1 online resource (119 p.)
225 1 $aSpringerBriefs in Mathematics,$x2191-8198
300   $aDescription based upon print version of record.
311   $a3-319-11706-8 
320   $aIncludes bibliographical references and index.
327   $a1 Introduction -- 2 Local dynamics of a parabolic germ -- 3 Global theory -- 4 Numerical results -- 5 For dessert: several amusing examples -- Index.
330   $aThis monograph grew out of the authors' efforts to provide a natural geometric description for the class of maps invariant under parabolic renormalization and for the Inou-Shishikura fixed point itself as well as to carry out a computer-assisted study of the parabolic renormalization operator. It introduces a renormalization-invariant class of analytic maps with a maximal domain of analyticity and rigid covering properties and presents a numerical scheme for computing parabolic renormalization of a germ, which is used to compute the Inou-Shishikura renormalization fixed point.   Inside, readers will find a detailed introduction into the theory of parabolic bifurcation,  Fatou coordinates, Écalle-Voronin conjugacy invariants of parabolic germs, and the definition and basic properties of parabolic renormalization.   The systematic view of parabolic renormalization developed in the book and the numerical approach to its study will be interesting to both experts in the field as well as graduate students wishing to explore one of the frontiers of modern complex dynamics.
410  0$aSpringerBriefs in Mathematics,$x2191-8198
606   $aDynamics
606   $aErgodic theory
606   $aFunctions of complex variables
606   $aNumerical analysis
606   $aDynamical Systems and Ergodic Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M1204X
606   $aFunctions of a Complex Variable$3https://scigraph.springernature.com/ontologies/product-market-codes/M12074
606   $aNumerical Analysis$3https://scigraph.springernature.com/ontologies/product-market-codes/M14050
615  0$aDynamics.
615  0$aErgodic theory.
615  0$aFunctions of complex variables.
615  0$aNumerical analysis.
615 14$aDynamical Systems and Ergodic Theory.
615 24$aFunctions of a Complex Variable.
615 24$aNumerical Analysis.
676   $a510
676   $a515.39
676   $a515.48
676   $a515.9
676   $a518
700   $aLanford III$b Oscar E$4aut$4http://id.loc.gov/vocabulary/relators/aut$01060590
702   $aYampolsky$b Michael$4aut$4http://id.loc.gov/vocabulary/relators/aut
906   $aBOOK
912   $a9910299991703321
996   $aFixed Point of the Parabolic Renormalization Operator$92514375
997   $aUNINA