↓ Skip to main content

Fractals and Chaos

Overview of attention for book
Cover of 'Fractals and Chaos'

Table of Contents

  1. Altmetric Badge
    Book Overview
  2. Altmetric Badge
    Chapter 1 Introduction to papers on quadratic dynamics: a progression from seeing to discovering
  3. Altmetric Badge
    Chapter 2 Acknowledgments related to quadratic dynamics
  4. Altmetric Badge
    Chapter 3 Fractal aspects of the iteration of z→λz(1-z) for complex λ and z
  5. Altmetric Badge
    Chapter 4 Cantor and Fatou dusts; self-squared dragons
  6. Altmetric Badge
    Chapter 5 The complex quadratic map and its ℳ-set
  7. Altmetric Badge
    Chapter 6 Bifurcation points and the “n-squared” approximation and conjecture, illustrated by M.L Frame and K Mitchell
  8. Altmetric Badge
    Chapter 7 The “normalized radical” of the ℳ-set
  9. Altmetric Badge
    Chapter 8 The boundary of the ℳ-set is of dimension 2
  10. Altmetric Badge
    Chapter 9 Certain Julia sets include smooth components
  11. Altmetric Badge
    Chapter 10 Domain-filling sequences of Julia sets, and intuitive rationale for the Siegel discs
  12. Altmetric Badge
    Chapter 11 Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets
  13. Altmetric Badge
    Chapter 12 Introduction to papers on chaos in nonquadratic dynamics: rational functions devised from doubling formulas
  14. Altmetric Badge
    Chapter 13 The map z → λ (z+1/z) and roughening of chaos, from linear to planar (computer-assisted homage to K. Hokusai)
  15. Altmetric Badge
    Chapter 14 Two nonquadratic rational maps devised from Weierstrass doubling formulas
  16. Altmetric Badge
    Chapter 15 Introduction to papers on Kleinian groups, their fractal limit sets, and IFS: history, recollections, and acknowledgments
  17. Altmetric Badge
    Chapter 16 Self-inverse fractals, Apollonian nets, and soap
  18. Altmetric Badge
    Chapter 17 Symmetry with respect to several circles: dilation/reduction, fractals, and roughness
  19. Altmetric Badge
    Chapter 18 Self-inverse fractals osculated by sigma-discs: the limit sets of (“Kleinian”) inversion groups
  20. Altmetric Badge
    Chapter 19 Introduction to measures that vanish exponentially almost everywhere: DLA and Minkowski
  21. Altmetric Badge
    Chapter 20 Invariant multifractal measures in chaotic Hamiltonian systems and related structures (Gutzwiller & M 1988)
  22. Altmetric Badge
    Chapter 21 The Minkowski measure and multifractal anomalies in invariant measures of parabolic dynamic systems
  23. Altmetric Badge
    Chapter 22 Harmonic measure on DLA and extended self-similarity (M & Evertsz 1991)
  24. Altmetric Badge
    Chapter 23 The inexhaustible function z squared plus c
  25. Altmetric Badge
    Chapter 24 The Fatou and Julia stories
  26. Altmetric Badge
    Chapter 25 Mathematical analysis while in the wilderness
Attention for Chapter 3: Fractal aspects of the iteration of z→λz(1-z) for complex λ and z
Altmetric Badge

Mentioned by

twitter
9 X users

Citations

dimensions_citation
191 Dimensions
You are seeing a free-to-access but limited selection of the activity Altmetric has collected about this research output. Click here to find out more.
Chapter title
Fractal aspects of the iteration of z→λz(1-z) for complex λ and z
Chapter number 3
Book title
Fractals and Chaos
Published by
Springer, New York, NY, January 2004
DOI 10.1007/978-1-4757-4017-2_3
Book ISBNs
978-1-4419-1897-0, 978-1-4757-4017-2
Authors

Benoit B. Mandelbrot

X Demographics

X Demographics

The data shown below were collected from the profiles of 9 X users who shared this research output. Click here to find out more about how the information was compiled.