The Hausdorff Dimension of Julia Sets of Meromorphic Functions II期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

The Hausdorff Dimension of Julia Sets of Meromorphic Functions II

Authors:	Stallard Gwyneth M.

Affiliation:	Department of Pure Mathematics, Open University Walton Hall, Milton Keynes MK7 6AA

Abstract:	A family of transcendental meromorphic functions, f_p(z), p $isin$ N is considered. It is shown that, if p $≥$ 6, then the Hausdorffdimension of the Julia set of ${lambda}$ f_p satisfies dim J( ${lambda}$ f_p) $≤$ 1/p, for0 < ${lambda}$ < 1/6^p, and dim J( ${lambda}$ f_p) $≥$ 1(30 ln ln p/ln p),for p^4p1/10⁵ ln p < ${lambda}$ < p^4p1/10⁴ ln p. Theseresults are used elsewhere to show that, for each d $isin$ (0, 1),there exists a transcendental meromorphic function for whichdim J(f) = d.

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