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＜電子ブック＞
Fixed Point of the Parabolic Renormalization Operator / by Oscar E. Lanford III, Michael Yampolsky
(SpringerBriefs in Mathematics. ISSN:21918201)

版	1st ed. 2014.
出版者	(Cham : Springer International Publishing : Imprint: Springer)
出版年	2014
本文言語	英語
大きさ	VIII, 111 p. 15 illus., 11 illus. in color : online resource
著者標目	*Lanford III, Oscar E author Yampolsky, Michael author SpringerLink (Online service)
件　名	LCSH:Dynamical systems LCSH:Functions of complex variables LCSH:Numerical analysis FREE:Dynamical Systems FREE:Functions of a Complex Variable FREE:Numerical Analysis
一般注記	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 expertsin the field as well as graduate students wishing to explore one of the frontiers of modern complex dynamics HTTP:URL=https://doi.org/10.1007/978-3-319-11707-2

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