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Fixed Point of the Parabolic Renormalization Operator by Michael Yampolsky
Fixed Point of the Parabolic Renormalization Operator by Michael Yampolsky
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Fixed Point of the Parabolic Renormalization Operator

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Description

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.
Release date Australia
November 17th, 2014
Audience
  • Postgraduate, Research & Scholarly
Illustrations
11 Illustrations, color; 4 Illustrations, black and white; VIII, 111 p. 15 illus., 11 illus. in color.
Pages
111
Dimensions
155x235x6
ISBN-13
9783319117065
Product ID
22762380

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