The multifractal analysis of Birkhoff averages for conformal repellers under random perturbations

Lin Shu

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The multifractal analysis of Birkhoff averages for conformal repellers under random perturbations

机译：随机扰动下共形驱蚊的伯克霍夫平均值的多重分形分析

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We study the stability of multifractal structures for dynamical systems under small perturbations. For a repeller associated with an expanding C 1+β -conformal topological mixing map, we show that the multifractal structure of Birkhoff averages is stable under small random perturbations. Keywords Birkhoff average - Bundle random dynamical system - Conformal repeller - Level sets - Multifractal analysis - Random perturbation - Spectrum Mathematics Subject Classification (2000) 28A78 - 28D20 - 60G57 Communicated by K. Schmidt.

机译：我们研究小扰动下动力系统的多重分形结构的稳定性。对于与扩展C 1 +β-保形拓扑混合图相关联的推斥器，我们表明Birkhoff平均数的多重分形结构在较小的随机扰动下是稳定的。关键字Birkhoff平均-捆绑随机动力系统-保形推斥子-水平集-多重分形分析-随机扰动-频谱数学主题分类（2000）28A78-28D20-60G57由K. Schmidt沟通。

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《Monatshefte für Mathematik》 |2010年第2期|p.81-113|共33页
作者
Lin Shu;
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正文语种 eng
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Birkhoff average; Bundle random dynamical system; Conformal repeller; Level sets; Multifractal analysis; Random perturbation; Spectrum;

机译：伯克霍夫平均;捆绑随机动力系统;保形排斥器;水平集;多重分形分析;随机扰动;光谱;

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1. The multifractal analysis of Birkhoff averages for conformal repellers under random perturbations [J] . Shu L. Monatshefte fur Mathematik . 2010,第1期

机译：随机扰动下共形驱蚊器的伯克霍夫平均值的多重分形分析
2. Multifractal analysis for Birkhoff averages on Lalley—Gatzouras repellers [J] . Henry W. J. Reeve Fundamenta Mathematicae . 2011,第1期

机译：Lalley-Gatzouras驱蚊器上Birkhoff平均值的多重分形分析
3. The Hausdorff dimension of average conformal repellers under random perturbation [J] . Zhao Y, Cao YL, Ban JC Nonlinearity . 2009,第10期

机译：随机扰动下普通保形驱避器的Hausdorff维数
4. Conformal frames and the validity of Birkhoff's theorem [C] . S. Capozziello, D. Saez-Gomez Spanish Relativity Meeting . 2011

机译：保形框架和Birkhoff的定理的有效性
5. Conformal Perturbations and Local Smoothing [D] . Muckerman, Dylan 2018

机译：保形摄动和局部平滑
6. Classifying acoustic signals into phoneme categories: average and dyslexic readers make use of complex dynamical patterns and multifractal scaling properties of the speech signal [O] . Fred Hasselman -1

机译：将声音信号分为音素类别：普通和阅读困难的读者利用语音信号的复杂动态模式和多重分形缩放特性
7. Multifractal analysis for Birkhoff averages on Lalley-Gatzouras repellers [O] . Reeve, Henry WJ 2011

机译：对Lalley-Gatzouras的Birkhoff平均值的多重分形分析 repellers
8. Random Perturbations of Dynamical Systems: Large Deviations and Averaging [R] . Freidlin, M. I. 1993

机译：动态系统的随机扰动：大偏差和平均

The multifractal analysis of Birkhoff averages for conformal repellers under random perturbations

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