On Lebesgue measure and Hausdorff dimension of Julia sets of real periodic points of renormalization

Calculating Hausdorff Dimension of Julia Sets and Kleinian Limit Sets

Area and Hausdorff Dimension of Julia Sets of Entire Functions

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Hausdorff Dimension and Conformal Measures of Feigenbaum Julia Sets

1.1. Statement of the results. One of the first questions usually asked about a fractal subset of R is whether it has the maximal possible Hausdorff dimension, n. It certainly happens if the set has positive Lebesgue measure. On the other hand, it is easy to construct fractal sets of zero measure but of dimension n. Moreover, this phenomenon is often observable for fractal sets produced by conf...

On the Hausdorff dimension of Julia sets of some real polynomials

The Hausdorff Dimension of Julia Sets of Entire Functions Iv

It is known that, for a transcendental entire function f, the Hausdorff dimension of J( f ) satisfies 1% dim J( f )% 2. For each d ` (1, 2), an example of a transcendental entire function f with dim J( f ) ̄ d is given. It is then indicated how this function can be modified to produce a transcendental meromorphic function F with one pole with dim J(F ) ̄ d. These appear to be the first examples o...