Universal Mandelbrot Set, The

Beginning Of The Story

Alexei Morozov (Itep, Russia), Valery Dolotin (Itep, Russia)

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Hardback

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English

World Scientific Publishing Co Pte Ltd
10 October 2006

Topology; Analytic topology

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.

By: Alexei Morozov (Itep Russia), Valery Dolotin (Itep, Russia)
Imprint: World Scientific Publishing Co Pte Ltd
Country of Publication: Singapore
Dimensions: Height: 232mm, Width: 161mm, Spine: 18mm
Weight: 449g
ISBN: 9789812568373
ISBN 10: 9812568379
Pages: 176
Publication Date: 10 October 2006
Audience: Professional and scholarly , Undergraduate
Format: Hardback
Publisher's Status: Active

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