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Hausdorff dimensions of the Julia sets of reluctantly recurrent rational maps

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Abstract

In this paper, we consider a rational map f of degree at least two acting on Riemman sphere that is expanding away from critical points. Assuming that all critical points of f in the Julia set J(f) are reluctantly recurrent, we prove that the Hausdorff dimension of the Julia set J(f) is equal to the hyperbolic dimension, and the Lebesgue measure of Julia set is zero when the Julia set J(f) ≠ .

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Authors and Affiliations

  1. School of Mathematics and Information Science, Henan University, Kaifeng, 475004, Henan Province, People’s Republic of China

    Huaibin Li

  2. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicuña Mackenna, 4860, Santiago, Chile

    Huaibin Li

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  1. Huaibin Li
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Correspondence to Huaibin Li.

Additional information

The author was supported by the National Natural Science Foundation of China (Grant No. 11101124) and proyecto FONDECYT grant 3110060 of Chile.

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Li, H. Hausdorff dimensions of the Julia sets of reluctantly recurrent rational maps. Indian J Pure Appl Math 44, 849–863 (2013). https://doi.org/10.1007/s13226-013-0046-3

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  • DOI: https://doi.org/10.1007/s13226-013-0046-3

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