1.

Record Nr.

UNINA9910299991703321

Autore

Lanford III Oscar E

Titolo

Fixed Point of the Parabolic Renormalization Operator [[electronic resource] /] / by Oscar E. Lanford III, Michael Yampolsky

Pubbl/distr/stampa

Cham : , : Springer International Publishing : , : Imprint : Springer, , 2014

ISBN

3-319-11707-6

Edizione

[1st ed. 2014.]

Descrizione fisica

1 online resource (119 p.)

Collana

SpringerBriefs in Mathematics, , 2191-8198

Disciplina

510

515.39

515.48

515.9

518

Soggetti

Dynamics

Ergodic theory

Functions of complex variables

Numerical analysis

Dynamical Systems and Ergodic Theory

Functions of a Complex Variable

Numerical Analysis

Lingua di pubblicazione

Inglese

Formato

Materiale a stampa

Livello bibliografico

Monografia

Note generali

Description based upon print version of record.

Nota di bibliografia

Includes bibliographical references and index.

Nota di contenuto

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

Sommario/riassunto

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.