Bounding the Area of the Mandelbrot Set
BibTeX
@MISC{Fisher_boundingthe,
author = {Yuval Fisher and Jay Hill},
title = {Bounding the Area of the Mandelbrot Set},
year = {}
}
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Abstract
Introduction. In considering the iteration of quadratic polynomials P c (z) = z 2 + c, where we denote the n-fold self composition of P c by P ffin c (z), the Mandelbrot set arises naturally. It is defined by M = fc j P ffin c (0) 6! 1 as n ! 1g: It is a compact subset of C which has received much popular as well as mathematical interest. Our goal is to estimate its area using complex analytic tools and a computer to carry out a numerical approximation. In a previous estimate, Ewing and Schober (1992) used the area theorem to compute an upper bound for the area of M . However, this estimate requires computing terms of the very slowly converging uniformization
Citations
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| 1 | Computing the Laurent Series of \Psi - Bielefeld, Fisher, et al. - 1988 |
| 1 | The area of the Mandelbrot - Ewing, Schober - 1992 |
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