Accepted:
20 Dec 2003
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/vol10/tomova02/ | © Copyright 2001 | |||
| Volume 10 | Received: Accepted: |
24 May 2001 20 Dec 2003 |
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Mandelbrot set for julia sets of arbitrary order - a remark on the shape of cubic mandelbrot and julia sets
Tomova, A. |
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| Abstract | |
| The Mandelbrot set for Julia sets,associated with fc (z) = z^2 + c,c in C is in detail very good studied.This family is of special importance because it provides a model for the onset of chaotic behaviour in physical and biological systems.Moreover it was the first family of dynamical systems for which a useful computergraphical map was constructed by Mandelbrot.In this paper we restrict the attention to the families:fc(z) = z^n + c ,fp,q(z) = z^3+ pz + q;c,p,q in C,n in N.We proof any theorems for the limits of Mandelbrot set for Julia sets of arbitrary order and for cubic Mandelbrot and Julia sets. We consider and make a remark on the shape of Mandelbrot and Julia sets for the dynamical systems in the general case fp,q(z) = z^n+ pz + q,n>3 too. | |
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Multimedia Links (none) Reference Links (none) Citation Reference Tomova, A. (2001), Mandelbrot set for julia sets of arbitrary order - a remark on the shape of cubic mandelbrot and julia sets, Complexity International, Volume 10, Paper ID: tomova02, URL: http://www.complexity.org.au/ci/vol10/tomova02/ |
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