Fractals and chaos : the mandelbrot set and beyond分形与混沌：Mandelbrot集与其它
点此进入淘宝搜索页搜索分类: 图书,进口原版书,科学与技术 Science & Techology ,
作者： Benoit B. Mandelbrot著
出 版 社：
出版时间： 2004-1-1字数：版次：页数： 308印刷时间： 2004/01/01开本： 16开印次：纸张： 胶版纸I S B N ： 9780387201580包装： 精装内容简介
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 This book contains the hard-to-obtain original papers, many unpublished illustrations dating back to 1979 and extensive documented historical context showing how Mandelbrot helped change our way of looking at the world.
目录
IQUADRATIC JULIA AND MANDELBROT SETS
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 -- Az(l-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 "n squared" approximation an conjecture (M1985g), illustrated by M.L. Frame and K. Mitchell
C7 The "normalized radical" 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)
Cll Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets (M1985n)
II NONQUADRATIC RATIONAL DYNAMICS
C12 Introduction to chaos in nonquadratic dynamics: rational functions devised from doubling formulas (2003)
C13 The map z -- 2~ (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 (1979-2003)
III ITERATED NONLINEAR FUNCTION SYSTEMS AND THE FRACTAL LIMIT SETS OF KLEINIAN GROUPS
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 CKleinian") groups (M1983m)
IV MULTIFRACTAL INVARIANT MEASURES
C19 Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski (2003)
C20 Invariant multifractal measures in chaotic Hamiltonian systems and related structures (GutzwiUer & 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)
V BACKGROUND AND HISTORY
C23 The inexhaustible function z squared plus c (1982-2003)
C24 The Fatou and Julia stories (2003)
C25 Mathematical analysis while in the wilderness (2003)
CUMULATIVE BIBLIOGRAPHY
INDEX
