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Titlebook: Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry; Volker Mayer,Mariusz Urbanski,Bartlomi

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发表于 2025-3-21 19:16:11 | 显示全部楼层 |阅读模式
书目名称Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry
编辑Volker Mayer,Mariusz Urbanski,Bartlomiej Skorulski
视频video
概述Contains new results.Complete treatment of the topic.Originality of the topic.Includes supplementary material:
丛书名称Lecture Notes in Mathematics
图书封面Titlebook: Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry;  Volker Mayer,Mariusz Urbanski,Bartlomi
描述.The theory of random dynamical systems originated from stochastic.differential equations. It is intended to provide a framework and.techniques to describe and analyze the evolution of dynamical.systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable expanding random dynamical systems, develop the thermodynamical formalism and establish, in particular, the exponential decay of correlations and analyticity of the expected pressure although the spectral gap property does not hold. This theory is then used to investigate fractal properties of conformal random systems. We prove a Bowen’s formula and develop the multifractal formalism of the Gibbs states. Depending on the behavior of the Birkhoff sums of the pressure function we arrive at a natural classification of the systems into two classes: quasi-deterministic systems, which share many.properties of deterministic ones; and essentially random systems, which are rather generic and never bi-Lipschitz equivalent to deterministic systems. We s
出版日期Book 2011
关键词37-XX; Hausdorff dimension; multifractal spectrum; random dynamical systems; thermodynamical formalism
版次1
doihttps://doi.org/10.1007/978-3-642-23650-1
isbn_softcover978-3-642-23649-5
isbn_ebook978-3-642-23650-1Series ISSN 0075-8434 Series E-ISSN 1617-9692
issn_series 0075-8434
copyrightSpringer-Verlag Berlin Heidelberg 2011
The information of publication is updating

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发表于 2025-3-21 21:50:22 | 显示全部楼层
发表于 2025-3-22 02:31:01 | 显示全部楼层
Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry
发表于 2025-3-22 05:14:52 | 显示全部楼层
Conclusion – Towards New Organizations?ee [9] and Question 5.4 in [8]) of whether the Hausdorff dimension of almost all (most) naturally defined random Julia sets is strictly larger than 1. We also show that in this same setting the Hausdorff dimension of almost all Julia sets is strictly less than 2.
发表于 2025-3-22 11:36:43 | 显示全部楼层
Classical Expanding Random Systems,ee [9] and Question 5.4 in [8]) of whether the Hausdorff dimension of almost all (most) naturally defined random Julia sets is strictly larger than 1. We also show that in this same setting the Hausdorff dimension of almost all Julia sets is strictly less than 2.
发表于 2025-3-22 13:37:02 | 显示全部楼层
发表于 2025-3-22 18:58:10 | 显示全部楼层
Barbara Stöttinger,Elfriede Penzxplain how this case can be reduced to random expanding maps by looking at an appropriate induced map. The picture is completed by providing and discussing a concrete map that is not expanding but expanding in the mean.
发表于 2025-3-23 00:57:22 | 显示全部楼层
Expanding in the Mean,xplain how this case can be reduced to random expanding maps by looking at an appropriate induced map. The picture is completed by providing and discussing a concrete map that is not expanding but expanding in the mean.
发表于 2025-3-23 03:32:27 | 显示全部楼层
Book 2011cribe and analyze the evolution of dynamical.systems when the input and output data are known only approximately, according to some probability distribution. The development of this field, in both the theory and applications, has gone in many directions. In this manuscript we introduce measurable ex
发表于 2025-3-23 08:16:44 | 显示全部楼层
The RPF-Theorem,thout any measurable structure on the space .. In particular, we do not address measurability issues of λ. and ... In order to obtain this measurability we will need and we will impose a natural measurable structure on the space .. This will be done in the next chapter.
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