Description

Book Synopsis

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.



Trade Review

“The book under review is devoted to the study of parabolic renormalization. … The book is very well written and self-contained … and most results are stated together with their proofs.” (Jasmin Raissy, zbMATH 1342.37051, 2016)



Table of Contents
​1 Introduction.- 2 Local dynamics of a parabolic germ.- 3 Global theory.- 4 Numerical results.- 5 For dessert: several amusing examples.- Index.

Fixed Point of the Parabolic Renormalization Operator

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    A Paperback by Oscar E. Lanford III, Michael Yampolsky

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      Book details

      Publisher Springer International Publishing AG
      Published 17 November 2014
      ISBN-13 9783319117065
      978-3319117065
      ISBN-10 3319117068
      Also in:
      Complex analysis, complex variables

      Description

      Book Synopsis

      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.



      Trade Review

      “The book under review is devoted to the study of parabolic renormalization. … The book is very well written and self-contained … and most results are stated together with their proofs.” (Jasmin Raissy, zbMATH 1342.37051, 2016)



      Table of Contents
      ​1 Introduction.- 2 Local dynamics of a parabolic germ.- 3 Global theory.- 4 Numerical results.- 5 For dessert: several amusing examples.- Index.

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