Fixed Point of the Parabolic Renormalization Operator
Language: English
Published by Palgrave Macmillan Nov 2014, 2014
- Softcover
- New
Seller: AHA-BUCH GmbH, Einbeck, GermanyAHA-BUCH GmbH
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Neuware - 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.…
Seller Inventory # 9783319117065
- Title
- Fixed Point of the Parabolic Renormalization Operator
- Author
- Oscar E. Lanford III
- Publisher
- Palgrave Macmillan Nov 2014
- Publication year
- 2014
- Condition
- Neu
- Binding
- Taschenbuch
- Language
- English
- ISBN 10
- 3319117068
- ISBN 13
- 9783319117065
- Item weight
- 195 grams
- Dimensions
- 235x155x7 mm
- Series
- Book 50 of 155: SpringerBriefs in Mathematics
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.
"Synopsis" may belong to another edition of this title.
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)
"About the title" may belong to another edition of this title.
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