Hausdorff dimensions of the Julia sets of reluctantly recurrent rational maps |
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| Authors: | Huaibin Li |
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| Institution: | 1. School of Mathematics and Information Science, Henan University, Kaifeng, 475004, Henan Province, People’s Republic of China
2. Facultad de Matemáticas, Pontificia Universidad Católica de Chile, Avenida Vicu?a Mackenna, 4860, Santiago, Chile
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| Abstract: | In this paper, we consider a rational map f of degree at least two acting on Riemman sphere ![src=]() 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) ≠ ![src=]() . |
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