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

  • Benoit B. Mandelbrot


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| < 1, are an intrinsic tiling that covers the interior of a f-set and rules the Schröder interpolation of the forward dynamics, its intrinsic inverse, and the periodic or chaotic limit properties of the intrinsic inverse.


Fundamental Domain Schroder Equation Arithmetic Property Forward Dynamic Siegel Disc 
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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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