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Universal Mandelbrot Set : Beginning of the Story by A. Morozov and V. Dolotin (2006, Hardcover)

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About this product

Product Identifiers

PublisherWorld Industries Scientific Publishing Co Pte LTD

ISBN-109812568379

ISBN-139789812568373

eBay Product ID (ePID)54242612

Product Key Features

Number of Pages162 Pages

Publication NameUniversal Mandelbrot Set : Beginning of the Story

LanguageEnglish

SubjectGeometry / General, Number Theory, Geometry / Algebraic

Publication Year2006

TypeTextbook

Subject AreaMathematics

AuthorA. Morozov, V. Dolotin

FormatHardcover

Dimensions

Item Height0.7 in

Item Weight15.9 Oz

Item Length9.1 in

Item Width6.3 in

Additional Product Features

Intended AudienceTrade

LCCN2006-049629

TitleLeadingThe

IllustratedYes

Dewey Decimal514.7

SynopsisThis 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, 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.

LC Classification NumberQA614.86.D65 2006