The map z → λ (z+1/z) and roughening of chaos, from linear to planar (computer-assisted homage to K. Hokusai)

  • Benoit B. Mandelbrot


The terms “chaos” and “order in chaos” prove extremely valuable but elude definition. It remains important to single out instances when the progress to planar chaos can be followed in a detailed and objective fashion. This paper proposes to show that an excellent such example is provided by the iterates of a map for which z and λ are both complex. The subject of this map is touched upon in M 1982F{FGN| but only on page 465, which was added in 1983, in the second printing. Therefore, the present paper is self-contained.


Fractal Dimension Real Interval Fractal Curve Logarithmic Spiral Siegel Disc 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Copyright information

© Benoit B. Mandelbrot 2004

Authors and Affiliations

  • Benoit B. Mandelbrot
    • 1
    • 2
  1. 1.Mathematics DepartmentYale UniversityNew HavenUSA
  2. 2.IBM T.J. Watson Research CenterYorktown HeightsUSA

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