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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.
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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...<br>
some time in the past (about 3/16/06 ):<br>
z'=(1-t)*(z^2+c)+t*(c*z^2+1)<br>
I think theirs is a parallel development, because I doubt they read
anything like newsgroups/ egroups, ha, ha...<br>
<br>
<a class="moz-txt-link-freetext"
href="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">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</a><b
class="sans">niversal Mandelbrot Set: Beginning of the Story
(Hardcover) </b><br>
by <a
href="http://www.amazon.com/exec/obidos/search-handle-url/104-0029617-0633535?%5Fencoding=UTF8&search-type=ss&index=books&field-author=V.%20Dolotin">V.
Dolotin</a> (Author), <a
href="http://www.amazon.com/exec/obidos/search-handle-url/104-0029617-0633535?%5Fencoding=UTF8&search-type=ss&index=books&field-author=A.%20Morozov">A.
Morozov</a> (Author), <a
href="http://www.amazon.com/exec/obidos/search-handle-url/104-0029617-0633535?%5Fencoding=UTF8&search-type=ss&index=books&field-author=A.%20D.%20Morozov">A.
D. Morozov</a> (Author)<br>
Product Summary<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.buy.com/prod/the-universal-mandelbrot-set-beginning-of-the-story/q/loc/106/202745831.html">http://www.buy.com/prod/the-universal-mandelbrot-set-beginning-of-the-story/q/loc/106/202745831.html</a><br>
<br>
<br>
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<br>
<br>
<a class="moz-txt-link-freetext"
href="http://www.worldscibooks.com/mathematics/6136.html">http://www.worldscibooks.com/mathematics/6136.html</a><br>
<br>
THE UNIVERSAL MANDELBROT SET<br>
Beginning of the Story<br>
<br>
by V Dolotin & A Morozov (ITEP, Russia)<br>
<br>
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.<br>
<br>
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.<br>
<br>
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.<br>
<br>
<br>
Contents:<br>
<br>
* Notions and Notation<br>
* Summary<br>
* Fragments of Theory<br>
* Map f(x) = X2 + c: From Standard Example to General
Conclusions <br>
<br>
<br>
<br>
Readership: Researchers and students in algebra & number theory and
mathematical physics. <br>
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