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Book Cover
Author Lanford, Oscar E., III, 1940-2013, author

Title Fixed point of the parabolic renormalization operator / Oscar E. Lanford III, Michael Yampolsky
Published Cham : Springer, [2014]
Online access available from:
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Description 1 online resource (viii, 111 pages) : illustrations (some color)
Series SpringerBriefs in Mathematics, 2191-8198
SpringerBriefs in mathematics.
Contents 1 Introduction -- 2 Local dynamics of a parabolic germ -- 3 Global theory -- 4 Numerical results -- 5 For dessert: several amusing examples -- Index
Summary 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
Bibliography Includes bibliographical references and index
Notes Online resource; title from PDF title page (SpringerLink, viewed November 20, 2014)
Subject Parabolic operators.
Fixed point theory.
Form Electronic book
Author Yampolsky, Michael, 1972- author
ISBN 3319117068 (print)
3319117076 (electronic bk.)
9783319117065 (print)
9783319117072 (electronic bk.)