On the dimensions of Cantor Julia sets of rational maps

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:402

Article

Zhai, Yu

关键词: Conformal dimension;    Conformal measure;    Hausdorff dimension;    Hyperbolic dimension;    Rational map;   

DOI  :  10.1016/j.jmaa.2013.01.052

来源: Elsevier

【 摘 要 】

In this paper, we study the dimensions associated with the Cantor Julia set of a rational map whose Fatou set is an attracting domain. We prove that if the Julia set of such a map contains no persistently recurrent critical points, then the conformal dimension and the Hausdorff dimension of the Julia set are equal. (c) 2013 Elsevier Inc. All rights reserved.

【 授权许可】

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