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

In: Fractals and Chaos

Author

Listed:
  • Benoit B. Mandelbrot

    (Yale University, Mathematics Department
    IBM T.J. Watson Research Center)

Abstract

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.

Suggested Citation

  • Benoit B. Mandelbrot, 2004. "The map z → λ (z+1/z) and roughening of chaos, from linear to planar (computer-assisted homage to K. Hokusai)," Springer Books, in: Fractals and Chaos, chapter 0, pages 146-156, Springer.
    • Handle: RePEc:spr:sprchp:978-1-4757-4017-2_13
    DOI: 10.1007/978-1-4757-4017-2_13
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