Tuesday, 17 July 2007

fractals - Hausdorff dimension of higher powers of the Mandebrot set ?

Yes, it does. See the full statement of Theorem 2 on page 6. The assumptions of the theorem are:




Suppose that a rational map f0 of degree d(>1) has a parabolic fixed
point ζ with multiplier exp(2πip/q) (p,qinmathbbZ,mathitgcd(p,q)=1) and that the immediate parabolic basin of ζ contains only one critical point of f0.




This is the case for zd+c.

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