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Fractals and chaos : the Mandelbrot set and beyond : selecta volume C

Author: Benoit B Mandelbrot
Publisher: New York : Springer, ©2004.
Edition/Format:   Print book : EnglishView all editions and formats
Database:WorldCat
Summary:
Publisher description: It has only been a couple of decades since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot set. That picture, now seeming graphically primitive, has changed our view of the mathematical and physical universe. The properties and circumstances of the discovery of the Mandelbrot Set continue to generate much interest in the research community and beyond. This  Read more...
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Material Type: Internet resource
Document Type: Book, Internet Resource
All Authors / Contributors: Benoit B Mandelbrot
ISBN: 0387201580 9780387201580
OCLC Number: 53477723
Description: xii, 308 pages : illustrations ; 24 cm
Contents: Foreword / by Peter W. Jones (2003) --
Preface (2003) --
I. Quadratic Julia and Mandelbrot sets. Introduction to papers on quadratic dynamics : a progression from seeing to discovering (2003) ; Acknowledgments related to quadratic dynamics (2003) ; Fractal aspects of the iteration of z [right pointing arrow symbol] [lambda] z (1-z) for complex [lambda] and z (M1980n) ; Cantor and Fatou dusts : self-squared dragons (M1982F) ; The complex quadratic map and its M-set (M1983p) ; Bifurcation points and the "n squared" approximation and conjecture (M1985g), illustrated by M.L. Frame and K. Mitchell ; The "normalized radical" of the M-set (Ml985g) ; The boundary of the M-set is of dimension 2 (M1985g) ; Certain Julia sets include smooth components (M1985g) ; Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs (M1985g) ; Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets (M1985n) --
II. Nonquadratic rational dynamics. Introduction to chaos in nonquadratic dynamics : rational functions devised from doubling formulas (2003) ; The map z [right pointing arrow symbol] [lambda] (z + 1/ z) and roughening of chaos from linear to planar (computer-assisted homage to K. Hokusai) (M1984k) ; Two nonquadratic rational maps, devised from Weierstrass doubling formulas (1979-2003) --
III. Iterated nonlinear function systems and the fractal limit sets of Kleinian groups. Introduction to papers on Kleinian groups, their fractal limit sets, and IFS : history, recollections, and acknowledgments (2003) ; Self-inverse fractals, Apollonian nets, and soap (M1982F) ; Symmetry by dilation or reduction, fractals, roughness (M2002w) ; Self-inverse fractals osculated by sigma-discs and limit sets of inversion ("Kleinian") groups (M1983m) --
IV. Multifractal invariant measures. Introduction to measures that vanish exponentially almost everywhere : DLA and Minkowski (2003) ; Invariant multifractal measures in chaotic Hamiltonian systems and related structures (Gutzwiller & M 1988) ; The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems (M1993s) ; Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991) --
V. Background and history. The inexhaustible function z squared plus c (1982-2003) ; The Fatou and Julia stories (2003) ; Mathematical analysis while in the wilderness (2003).
Responsibility: Benoit B. Mandelbrot ; with a foreword by P.W. Jones and texts co-authored by C.J.G. Evertsz and M.C. Gutzwiller.
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Offers papers related to the famous inkblot figure, Mandelbrot set.  Read more...

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From the reviews: "It is only twenty-three years since Benoit Mandelbrot published his famous picture of what is now called the Mandelbrot Set. The graphics were state of the art, though now they may Read more...

 
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