1 option
Fixed Point of the Parabolic Renormalization Operator / by Oscar E. Lanford III, Michael Yampolsky.
Springer Nature - Springer Mathematics and Statistics (R0) eBooks 2014 English International Available online
View online- Format:
- Book
- Author/Creator:
- Lanford III, Oscar E., Author.
- Yampolsky, Michael., Author.
- Series:
- SpringerBriefs in Mathematics, 2191-8198
- Language:
- English
- Subjects (All):
- Dynamics.
- Ergodic theory.
- Functions of complex variables.
- Numerical analysis.
- Dynamical Systems and Ergodic Theory.
- Functions of a Complex Variable.
- Numerical Analysis.
- Local Subjects:
- Dynamical Systems and Ergodic Theory.
- Functions of a Complex Variable.
- Numerical Analysis.
- Physical Description:
- 1 online resource (119 p.)
- Edition:
- 1st ed. 2014.
- Place of Publication:
- Cham : Springer International Publishing : Imprint: Springer, 2014.
- Language Note:
- English
- 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.
- Contents:
- 1 Introduction
- 2 Local dynamics of a parabolic germ
- 3 Global theory
- 4 Numerical results
- 5 For dessert: several amusing examples
- Index.
- Notes:
- Description based upon print version of record.
- Includes bibliographical references and index.
- ISBN:
- 3-319-11707-6
The Penn Libraries is committed to describing library materials using current, accurate, and responsible language. If you discover outdated or inaccurate language, please fill out this feedback form to report it and suggest alternative language.