Universal Mandelbrot Set: Beginning of the Story,by V. Dolotin , A. D. Morozov

[Roger Bagula]

Form the cover these fellows seem to have published on my idea of a
Riddled/ Beziered Mandelbrot set/ Fiegenbauk\m set which I posted here...
some time in the past (about 3/16/06 ):
z'=(1-t)*(z^2+c)+t*(c*z^2+1)
I think theirs is a parallel development, because I doubt they read
anything like newsgroups/ egroups, ha, ha...

http://www.amazon.com/Universal-Mandelbrot-Set-Beginning-Story/dp/9812568379/ref=sr_1_1/104-0029617-0633535?ie=UTF8&s=books&qid=1174853320&sr=8-1*niversal
Mandelbrot Set: Beginning of the Story (Hardcover) *
by V. Dolotin
<http://www.amazon.com/exec/obidos/search-handle-url/104-0029617-0633535?%5Fencoding=UTF8&search-type=ss&index=books&field-author=V.%20Dolotin>
(Author), A. Morozov
<http://www.amazon.com/exec/obidos/search-handle-url/104-0029617-0633535?%5Fencoding=UTF8&search-type=ss&index=books&field-author=A.%20Morozov>
(Author), A. D. Morozov
<http://www.amazon.com/exec/obidos/search-handle-url/104-0029617-0633535?%5Fencoding=UTF8&search-type=ss&index=books&field-author=A.%20D.%20Morozov>
(Author)
Product Summary

http://www.buy.com/prod/the-universal-mandelbrot-set-beginning-of-the-story/q/loc/106/202745831.html


This book is devoted to the structure of the Mandelbrot set--a
remarkable and important feature of modern theoretical physics, related
to chaos and fractals and simultaneously to analytical functions,
Riemann surfaces, phase transitions and string theory. The Mandelbrot
set is one of the bridges connecting the world of chaos and order. The
authors restrict consideration to

http://www.worldscibooks.com/mathematics/6136.html

THE UNIVERSAL MANDELBROT SET
Beginning of the Story

by V Dolotin & A Morozov (ITEP, Russia)

This book is devoted to the structure of the Mandelbrot set -- a
remarkable and important feature of modern theoretical physics, related
to chaos and fractals and simultaneously to analytical functions,
Riemann surfaces, phase transitions and string theory. The Mandelbrot
set is one of the bridges connecting the world of chaos and order.

The authors restrict consideration to discrete dynamics of a single
variable. This restriction preserves the most essential properties of
the subject, but drastically simplifies computer simulations and the
mathematical formalism.

The coverage includes a basic description of the structure of the set of
orbits and pre-orbits associated with any map of an analytic space into
itself. A detailed study of the space of orbits (the algebraic Julia
set) as a whole, together with related attributes, is provided. Also
covered are: moduli space in the space of maps and the classification
problem for analytic maps, the relation of the moduli space to the
bifurcations (topology changes) of the set of orbits, a combinatorial
description of the moduli space (Mandelbrot and secondary Mandelbrot
sets) and the corresponding invariants (discriminants and resultants),
and the construction of the universal discriminant of analytic functions
in terms of series coefficients. The book concludes by solving the case
of the quadratic map using the theory and methods discussed earlier.


Contents:

* Notions and Notation
* Summary
* Fragments of Theory
* Map f(x) = X2 + c: From Standard Example to General Conclusions



Readership: Researchers and students in algebra & number theory and
mathematical physics.

[Roger Bagula]

If somebody here has read the book,
please put up a reader review at:
http://www.amazon.com/Universal-Mandelbrot-Set-Beginning-Story/dp/9812568379/ref=sr_1_1/104-0029617-0633535?ie=UTF8&s=books&qid=1174853419&sr=1-1

And let us know what you think of it!