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|Material Type:||Internet resource|
|Document Type:||Book, Internet Resource|
|All Authors / Contributors:||
Benoit B Mandelbrot
|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.|
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