Fixed Point of the Parabolic Renormalization Operator - SpringerBriefs in Mathematics - Oscar E. Lanford III - Books - Springer International Publishing AG - 9783319117065 - November 17, 2014
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Oscar E. Lanford III
Fixed Point of the Parabolic Renormalization Operator - SpringerBriefs in Mathematics 2014 edition

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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.

111 pages, 4 black & white illustrations, 11 colour illustrations, biography

Media Books     Paperback Book   (Book with soft cover and glued back)
Released November 17, 2014
ISBN13 9783319117065
Publishers Springer International Publishing AG
Pages 111
Dimensions 155 × 235 × 6 mm   ·   176 g
Language English  

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