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摘要翻译：
考虑概率空间的可逆保测度变换。如果这个空间的有限划分在变换幂次下有无限多个联合独立的像，那么这个空间的有限划分称为弱独立的。Krengel证明了一个变换是弱混合的当且仅当下空间的弱独立分块在所有有限分块中是稠密的。利用del Junco-Reinhold-Weiss和del Junco-Begin，我们得到了弱混合随机动力系统（或等效地，相对弱混合的斜积）的Krengel型结果。
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英文标题：
《Partitions with independent iterates in random dynamical systems》
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作者：
Boris Begun, Andres del Junco
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最新提交年份：
2007
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分类信息：
一级分类：Mathematics 数学
二级分类：Dynamical Systems 动力系统
分类描述：Dynamics of differential equations and flows, mechanics, classical few-body problems, iterations, complex dynamics, delayed differential equations
微分方程和流动的动力学，力学，经典的少体问题，迭代，复杂动力学，延迟微分方程
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一级分类：Mathematics 数学
二级分类：Commutative Algebra 交换代数
分类描述：Commutative rings, modules, ideals, homological algebra, computational aspects, invariant theory, connections to algebraic geometry and combinatorics
交换环，模，理想，同调代数，计算方面，不变理论，与代数几何和组合学的联系
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一级分类：Mathematics 数学
二级分类：Algebraic Geometry 代数几何
分类描述：Algebraic varieties, stacks, sheaves, schemes, moduli spaces, complex geometry, quantum cohomology
代数簇，叠，束，格式，模空间，复几何，量子上同调
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一级分类：Mathematics 数学
二级分类：Analysis of PDEs 偏微分方程分析
分类描述：Existence and uniqueness, boundary conditions, linear and non-linear operators, stability, soliton theory, integrable PDE's, conservation laws, qualitative dynamics
存在唯一性，边界条件，线性和非线性算子，稳定性，孤子理论，可积偏微分方程，守恒律，定性动力学
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英文摘要：
Consider an invertible measure-preserving transformation of a probability space. A finite partition of the space is called weakly independent if there are infinitely many images of this partition under powers of the transformation that are jointly independent. Krengel proved that a transformation is weakly mixing if and only if weakly independent partitions of the underlying space are dense among all finite partitions. Using the tools developed in the later papers of del Junco-Reinhold-Weiss and del Junco-Begun we obtain Krengel- type results for weakly mixing random dynamical systems (or equivalently, skew products that are relatively weakly mixing).
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PDF链接：
https://arxiv.org/pdf/0706.1607
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