Click Here to Download: https://ouo.io/w5nP5W Fixed Point of the Parabolic Renormalization Operator By: Oscar E. Lanford III; Michael Yampolsky Publisher: Springer Print ISBN: 9783319117065, 3319117068 eText ISBN: 9783319117072, 3319117076 Copyright year: 2014 Format: EPUB Available from $ 69.99 USD SKU 9783319117072 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.
