EAN: 9783319117065

SPRINGERBRIEFS IN MATHEMATICS FIXED POINT OF ...

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.

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