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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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發(fā)表于 2025-3-21 19:16:11 | 只看該作者 |倒序?yàn)g覽 |閱讀模式
書目名稱Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry
編輯Volker Mayer,Mariusz Urbanski,Bartlomiej Skorulski
視頻videohttp://file.papertrans.cn/282/281664/281664.mp4
概述Contains new results.Complete treatment of the topic.Originality of the topic.Includes supplementary material:
叢書名稱Lecture Notes in Mathematics
圖書封面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
關(guān)鍵詞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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沙發(fā)
發(fā)表于 2025-3-21 21:50:22 | 只看該作者
板凳
發(fā)表于 2025-3-22 02:31:01 | 只看該作者
Distance Expanding Random Mappings, Thermodynamical Formalism, Gibbs Measures and Fractal Geometry
地板
發(fā)表于 2025-3-22 05:14:52 | 只看該作者
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.
5#
發(fā)表于 2025-3-22 11:36:43 | 只看該作者
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.
6#
發(fā)表于 2025-3-22 13:37:02 | 只看該作者
7#
發(fā)表于 2025-3-22 18:58:10 | 只看該作者
Barbara St?ttinger,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.
8#
發(fā)表于 2025-3-23 00:57:22 | 只看該作者
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.
9#
發(fā)表于 2025-3-23 03:32:27 | 只看該作者
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
10#
發(fā)表于 2025-3-23 08:16:44 | 只看該作者
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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