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

Benoit B. Mandelbrot
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Benoit B. Mandelbrot: Yale University, Mathematics Department

Chapter C13 in Fractals and Chaos, 2004, pp 146-156 from Springer

Abstract: 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.

Keywords: Fractal Dimension; Real Interval; Fractal Curve; Logarithmic Spiral; Siegel Disc (search for similar items in EconPapers)
Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-1-4757-4017-2_13

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DOI: 10.1007/978-1-4757-4017-2_13

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