Fractals and Chaos
Benoit B. Mandelbrot
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Benoit B. Mandelbrot: Yale University, Mathematics Department
in Springer Books from Springer
Date: 2004
ISBN: 978-1-4757-4017-2
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Chapters in this book:
- Ch C1 Introduction to papers on quadratic dynamics: a progression from seeing to discovering
- Benoit B. Mandelbrot
- Ch C10 Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs
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- Ch C11 Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets
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- Ch C12 Introduction to papers on chaos in nonquadratic dynamics: rational functions devised from doubling formulas
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- Ch C13 The map z → λ (z+1/z) and roughening of chaos, from linear to planar (computer-assisted homage to K. Hokusai)
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- Ch C14 Two nonquadratic rational maps devised from Weierstrass doubling formulas
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- Ch C15 Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments
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- Ch C16 Self-inverse fractals, Apollonian nets, and soap
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- Ch C17 Symmetry with respect to several circles: dilation/reduction, fractals, and roughness
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- Ch C18 Self-inverse fractals osculated by sigma-discs: the limit sets of (“Kleinian”) inversion groups
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- Ch C19 Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski
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- Ch C2 Acknowledgments related to quadratic dynamics
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- Ch C20 Invariant multifractal measures in chaotic Hamiltonian systems and related structures (Gutzwiller & M 1988)
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- Ch C21 The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems
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- Ch C22 Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991)
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- Ch C23 The inexhaustible function z squared plus c
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- Ch C24 The Fatou and Julia stories
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- Ch C25 Mathematical analysis while in the wilderness
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- Ch C3 Fractal aspects of the iteration of z→λz(1-z) for complex λ and z
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- Ch C4 Cantor and Fatou dusts; self-squared dragons
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- Ch C5 The complex quadratic map and its ℳ-set
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- Ch C6 Bifurcation points and the “n-squared” approximation and conjecture, illustrated by M.L Frame and K Mitchell
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- Ch C7 The “normalized radical” of the ℳ-set
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- Ch C8 The boundary of the ℳ-set is of dimension 2
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- Ch C9 Certain Julia sets include smooth components
- Benoit B. Mandelbrot
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DOI: 10.1007/978-1-4757-4017-2
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