Computing multifractal spectra

D. Kagiso; M. Pollicott

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Computing multifractal spectra

机译：计算多重分形光谱

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The famous Birkhoff ergodic theorem shows that given an ergodic measure the averages of an integrable function along typical orbits converge to the integral of the function. The multifractal spectra describe the sets of points for which the averages converge to another limit. In this note, we will consider the specific setting of conformal repellers and show how to estimate the Hausdorff dimensions of such sets via approximations to their alternative characterizations as zeros of appropriate determinant functions.

机译：著名的伯克霍夫（Birkhoff）遍历定理表明，给定遍历度度量，沿着典型轨道的可积函数的平均值收敛到该函数的积分。多重分形光谱描述了平均值收敛到另一个极限的点集。在本说明中，我们将考虑共形驱虫剂的具体设置，并展示如何通过近似估计其可替代行列式为适当行列式函数的零来估计此类集合的Hausdorff尺寸。

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来源
《Dynamical Systems》 |2015年第4期|404-425|共22页
作者
D. Kagiso; M. Pollicott;
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作者单位

Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK;

Mathematics Institute, University of Warwick, Coventry, CV4 7AL, UK;

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收录信息美国《科学引文索引》(SCI);美国《工程索引》(EI);美国《生物学医学文摘》(MEDLINE);美国《化学文摘》(CA);
原文格式 PDF
正文语种 eng
中图分类
关键词
Hausdorff dimension; multifractal; Birkhoff Ergodic theorem;

机译：Hausdorff尺寸;分形伯克霍夫遍历定理;

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Computing multifractal spectra

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