Item description for Universal Mandelbrot Set: Beginning of the Story by V. Dolotin & A. Morozov...
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.
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Studio: World Scientific Publishing Company
Est. Packaging Dimensions: Length: 9.06" Width: 6.14" Height: 0.71" Weight: 0.93 lbs.
Release Date Oct 9, 2006
Publisher World Scientific Publishing Company
ISBN 9812568379 ISBN13 9789812568373
Reviews - What do customers think about Universal Mandelbrot Set: Beginning of the Story?
Are generalized Mandelbrot sets 2 dimensional borders? Apr 20, 2007
I have been doing Beziers of Mandelbrot sets for over ten years. After just seeing the cover of this book I was inspired to experiment with Beziers and Riddle rotation transforms of Feigenbaum sets with Mandelbrot sets. Many of us have noticed the n to n-1 relationship in Julia sets to generalized Mandelbrot sets. I had discovered a German Internet site with the Cubic Julias on page 103 ( fig, 5.18) and have on my own refined the relationship in IFS as I have for years striven to get a Mandelbrot set Iterated Function system! The book has no index and the authors seem only vaguely familiar with the extensive western complex dynamics literatureComplex Dynamics (Universitext / Universitext: Tracts in Mathematics) ( only 12 bibliographic notes).Despite the sausage Mandelbrot and and belted pillow Julia metaphors at the end I think that the book is inspired and it will take me years to run all the experiments on a computer that it suggests to me. Fresh Fish is a good thing with the stale eastern doctrine weighing down the new science! Maybe the second edition with have an index?