Continuous interpolation of the quadratic map and intrinsic tiling of the interiors of Julia sets

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

Chapter C11 in Fractals and Chaos, 2004, pp 125-136 from Springer

Abstract: Abstract This work reports several observations concerning the dynamics of a continuous interpolate, forward and backward, of the quadratic map of the complex plane. In the difficult limit case |λ| = 1, the dynamics is known to have rich structures that depend on whether arg λ/2π is rational or a Siegel number. This paper establishes that these structures, a counterpart for |λ|

Keywords: Fundamental Domain; Schroder Equation; Arithmetic Property; Forward Dynamic; 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_11

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DOI: 10.1007/978-1-4757-4017-2_11

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