Universal Mandelbrot Set, The: Beginning Of The Story
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A01=Alexei Morozov
A01=Valery Dolotin
Author_Alexei Morozov
Author_Valery Dolotin
Bifurcation
Category=PBH
Category=PBMW
Category=PBPH
Category=PH
Discrete Dynamics
Discriminant
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eq_nobargain
eq_non-fiction
eq_science
Julia Set
Mandelbrot Set
Orbits
Resultant
Product details
- ISBN 9789812568373
- Publication Date: 10 Oct 2006
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
