The Hausdorff dimension of the Julia sets concerning renormalization transformation

Gao Junyang

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The Hausdorff dimension of the Julia sets concerning renormalization transformation

机译：Julia集的Hausdorff维数涉及重归一化变换

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We consider a family of rational maps T-n,T-lambda of lambda-state diamond-like hierarchical Potts models concerning renormalization transformation. We give an asymptotic formula of the Hausdorff dimension of the Julia sets j(T-n,T-lambda) for sufficiently large lambda. (C) 2015 Elsevier Ltd. All rights reserved.

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《Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science》 |2015年第null期|共6页
作者
Gao Junyang;
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正文语种 eng
中图分类动力系统理论;
关键词
Hausdorff dimension; Julia set; Conjugation; Renormalization transformation;

机译：Hausdorff维数;Julia集;共轭;重整化变换;

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1. The Hausdorff dimension of the Julia sets concerning renormalization transformation [J] . Gao Junyang Chaos, Solitons and Fractals: Applications in Science and Engineering: An Interdisciplinary Journal of Nonlinear Science . 2015,第Null期

机译：Julia集的Hausdorff维数涉及重归一化变换
2. Calculating Hausdorff dimension of Julia sets and Kleinian limit sets [J] . Jenkinson O., Pollicott M. American Journal of Mathematics . 2002,第3期

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3. Hausdorff dimensions of the Julia sets of reluctantly recurrent rational maps [J] . Huaibin Li Indian Journal of Pure and Applied Mathematics . 2013,第6期

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4. A Comparison of Fractal Dimension Estimations for Filled Julia Fractal Sets Based on the Escape Time Algorithm [C] . Arkan Jassim Mohammed International Conference of Mathematical Sciences . 2019

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5. Conformal dimension of Cantor sets and curve families in the plane: Central sets of Hausdorff dimension 2. [D] . Hakobyan, Hrant. 2006

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8. Continuity of Hausdorff Dimension of Julia-Lavaurs Sets as a Function of thePhase [R] . Urbanski, M., Zinsmeister, M. 2000

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The Hausdorff dimension of the Julia sets concerning renormalization transformation

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