Keller, K.

Invariant Factors, Julia Equivalences and the (abstract) Mandelbrot Set

Lecture Notes in Mathematics, Vol. 1732:
This book is mainly devoted to the combinatorics of quadratic
holomorphic dynamics.
The conceptual kernel is a self-contained abstract counterpart of
connected quadratic Julia sets which is built on Thurston's concept
of a quadratic invariant lamination and on symbolic descriptions
of the angle-doubling map.
The theory obtained is illustrated in the complex plane.
It is used to give rigorous proofs of some well-known and some
partially new statements on the structure of the Mandelbrot set.
May 2000 205 pp.
3-540-67434-9

Tim Hsu

Quilts: Central Extensions, Braid Actions, & Finite Groups

Lecture Notes in Mathematics,Vol. 1731:
Quilts are 2-complexes used to analyze actions and subgroups
of the 3-string braid group and similar groups.
This monograph establishes the fundamentals of quilts and discusses
connections with central extensions, braid actions, and finite groups.
Most results have not previously appeared in a widely available form,
and many results appear in print for the first time.
This monograph is accessible to graduate students, as a substantial
amount of background material is included.
The methods and results may be relevant to researchers interested
in infinite groups, moonshine, central extensions, triangle groups,
dessins deonfants, and monodromy actions of braid groups.
May 2000 185 pp.
3-540-67397-0

Graf, S. /Luschgy, H.

Foundations of Quantization for Probability Distributions

Lecture Notes in Mathematics, Vol. 1730:
Due to the rapidly increasing need for methods of data compression,
quantization has become a flourishing field in signal and image
processing and information theory. The same techniques are also
used in statistics (cluster analysis), pattern recognition,
and operations research (optimal location of service centers).
The book gives the first mathematically rigorous account of the
fundamental theory underlying these applications.
The emphasis is on the asymptotics of quantization errors for
absolu-tely continuous and special classes of singular probabilities
(surface measures, self-similar measures) presenting some
new results for the first time.
June 2000 230 pp.
3-540-67394-6
Springer