The Hausdorff Dimension of Julia Sets of Entire Functions Iv
نویسنده
چکیده
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 of Julia sets with non-integer dimensions whose dimensions have been calculated exactly.
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