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Titlebook: Ergodic Theory of Random Transformations; Yuri Kifer Book 1986 Springer Science+Business Media New York 1986 differential equation.dynamic

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发表于 2025-3-21 18:40:47 | 显示全部楼层 |阅读模式
书目名称Ergodic Theory of Random Transformations
编辑Yuri Kifer
视频videohttp://file.papertrans.cn/315/314498/314498.mp4
丛书名称Progress in Probability
图书封面Titlebook: Ergodic Theory of Random Transformations;  Yuri Kifer Book 1986 Springer Science+Business Media New York 1986 differential equation.dynamic
描述Ergodic theory of dynamical systems i.e., the qualitative analysis of iterations of a single transformation is nowadays a well developed theory. In 1945 S. Ulam and J. von Neumann in their short note [44] suggested to study ergodic theorems for the more general situation when one applies in turn different transforma­ tions chosen at random. Their program was fulfilled by S. Kakutani [23] in 1951. ‘Both papers considered the case of transformations with a common invariant measure. Recently Ohno [38] noticed that this condition was excessive. Ergodic theorems are just the beginning of ergodic theory. Among further major developments are the notions of entropy and characteristic exponents. The purpose of this book is the study of the variety of ergodic theoretical properties of evolution processes generated by independent applications of transformations chosen at random from a certain class according to some probability distribution. The book exhibits the first systematic treatment of ergodic theory of random transformations i.e., an analysis of composed actions of independent random maps. This set up allows a unified approach to many problems of dynamical systems, products of random
出版日期Book 1986
关键词differential equation; dynamical systems; ergodic theory; probability; probability distribution; stochast
版次1
doihttps://doi.org/10.1007/978-1-4684-9175-3
isbn_softcover978-1-4684-9177-7
isbn_ebook978-1-4684-9175-3Series ISSN 1050-6977 Series E-ISSN 2297-0428
issn_series 1050-6977
copyrightSpringer Science+Business Media New York 1986
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发表于 2025-3-21 21:01:39 | 显示全部楼层
1050-6977 e., an analysis of composed actions of independent random maps. This set up allows a unified approach to many problems of dynamical systems, products of random 978-1-4684-9177-7978-1-4684-9175-3Series ISSN 1050-6977 Series E-ISSN 2297-0428
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https://doi.org/10.1007/978-3-662-61025-145 S. Ulam and J. von Neumann in their short note [44] suggested to study ergodic theorems for the more general situation when one applies in turn different transformations chosen at random. Their program was fulfilled by S. Kakutani [23] in 1951. ‘Both papers considered the case of transformations
发表于 2025-3-22 13:00:23 | 显示全部楼层
https://doi.org/10.1007/978-3-662-61005-3nd topological entropies for compositions of random maps. These entropies turn out to be the “mixed” or “relative” entropies of Abramov-Rohlin [l] and Ledrappier-Walters [32] corresponding to the skew product transformation . but our motivation and the set up are different from theirs. We shall revi
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,Einführung in die Nachhaltigkeit,In this chapter we study basic connections between compositions of independent random transformations and corresponding Markov chains together with some applications.
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https://doi.org/10.1007/978-3-662-61001-5In this chapter we shall prove some kind of the multiplicative ergodic theorem which describes growth rates of the norms of vectors under the actions of compositions of independent random bundle maps.
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https://doi.org/10.1007/978-3-658-29433-5Under mild additional hypothesis we shall be able to prove the continuity of invariant subbundles constructed in the previous chapter. Then we shall establish conditions providing stability and positivity of the biggest characteristics exponent.
发表于 2025-3-23 07:00:51 | 显示全部楼层
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