Fractals and chaos. The Mandelbrot set and beyond

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 “n squared” approximation and 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) — 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 (1979-2003) — 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 (“Kleinian”) 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 (1982-2003) — C24 The Fatou and Julia stories (2003) — C25 Mathematical analysis while in the wilderness (2003) — Cumulative Bibliography.;”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 seem primitive. But how that picture has changed our views of the mathematical and physical universe! Fractals, a term coined by Mandelbrot, are now so ubiquitous in the scientific conscience that it is difficult to remember the psychological shock of their arrival. What we see in this book is a glimpse of how Mandelbrot helped change our way of looking at the world. It is not just a book about a particular class of problems, but contains a view on how to approach the mathematical and physical universe. This view is certain not to fade, but to be part of the working philosophy of the next mathematical revolution, wherever it may take us. So read the book, look at the beautiful pictures that continue to fascinate and amaze, and enjoy! ” From the foreword by Peter W Jones, Yale University This heavily illustrated book combines hard-to-find early papers by the author with additional chapters that describe the historical background and context. Key topics are quadratic dynamics and its Julia and Mandelbrot sets, nonquadratic dynamics, Kleinian limit sets, and the Minkowski measure. Benoit B Mandelbrot is Sterling Professor of Mathematical Sciences at Yale University and IBM Fellow Emeritus (Physics) at the IBM T J Watson Research Center. He was awarded the Wolf Prize for Physics in 1993 and the Japan Prize for Science and Technology in 2003.

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.

Title: Fractals and Chaos The Mandelbrot Set and Beyond
ISBN: 0387201580,9780387201580
Publisher: Springer Science & Business Media
Genre: Mathematics / General
Date Published:
Pages: 308
Preview Link: Google Preview Link

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