Author | Mandelbrot, Benoit B. author |
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Title | Fractals and Chaos [electronic resource] : The Mandelbrot Set and Beyond / by Benoit B. Mandelbrot |
Imprint | New York, NY : Springer New York : Imprint: Springer, 2004 |
Connect to | http://dx.doi.org/10.1007/978-1-4757-4017-2 |
Descript | XII, 308 p. online resource |
List of Chapters -- C1 Introduction to papers on quadratic dynamics: a progression from seeing to discovering (2003) -- C2 Acknowledgments related to quadratic dynamics (2003) -- C3 Fractal aspects of the iteration of z ? ? z (1-z) for complex A and z (M1980n) -- C4 Cantor and Fatou dusts; self-squared dragons (M 1982F) -- C5 The complex quadratic map and its M-set (M1983p) -- C6 Bifurcation points and the โn squaredโ approximation and conjecture (M1985g), illustrated by M.L Frame and K Mitchell -- C7 The โnormalized radicalโ of the M-set (M1985g) -- C8 The boundary of the M-set is of dimension 2 (M1985g) -- C9 Certain Julia sets include smooth components (M1985g) -- C10 Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs (M1985g) -- C11 Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets (M1985n) -- C12 Introduction to chaos in nonquadratic dynamics: rational functions devised from doubling formulas (2003) -- C13 The map z ? ? (z + 1/z) and roughening of chaos from linear to planar (computer-assisted homage to K Hokusai) (M1984k) -- C14 Two nonquadratic rational maps, devised from Weierstrass doubling formulas (1979โ2003) -- C15 Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments (2003) -- C16 Self-inverse fractals, Apollonian nets, and soap (M 1982F) -- C17 Symmetry by dilation or reduction, fractals, roughness (M2002w) -- C18 Self-inverse fractals osculated by sigma-discs and limit sets of inversion (โKleinianโ) groups (M1983m) -- C19 Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski (2003) -- C20 Invariant multifractal measures in chaotic Hamiltonian systems and related structures (Gutzwiller & M 1988) -- C21 The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems (M1993s) -- C22 Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991) -- C23 The inexhaustible function z squared plus c (1982โ2003) -- C24 The Fatou and Julia stories (2003) -- C25 Mathematical analysis while in the wilderness (2003) -- Cumulative Bibliography