Periodic points of complex quadratic mappings





definition
Zpperiodic points of  Complex quadratic (Mandelbrot) map  when :
Zp = Fc(n)(Zp)
 where n = period

so they are roots of polynomials ( = solutions of polynomial equations) of degree 2 * n
Fc(n)(Zp) - Zp = 0

As Brian Towles explains on sci.fractals :
F(z) = z       [equation for points with period 1 which is 2nd order polynomial ]
F(F(z)) = z      [equation for points with period 2, 4th order polynomial ]
.
F(F(F(...F(z)...)))) = z    [equation for period n, 2^n order polynomial ]


Only polynomial equations of degree 4 ( quartic ) or less can be solved explicitly.


see also:


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Autor: Adam Majewski
adammaj1-at-o2-dot-pl
Feel free to e-mail me. (:-))

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