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.