The entropy of a skew product of measure-preserving transformations

1965 ◽  
pp. 255-265 ◽  
Author(s):  
L. M. Abramov ◽  
V. A. Rohlin
Keyword(s):  
Skew Product ◽  
Measure Preserving Transformations

scholarly journals Mixing properties of induced random transformations

1997 ◽  
Vol 17 (4) ◽  
pp. 839-847 ◽  
Author(s):  
HANS-OTTO GEORGII
Keyword(s):  
Random Walk ◽  
Abelian Group ◽  
Probability Space ◽  
Return Time ◽  
Skew Product ◽  
Mixing Properties ◽  
Countable Abelian Group ◽  
Measure Preserving Transformations

Let $S(N)$ be a random walk on a countable abelian group $G$ which acts on a probability space $E$ by measure-preserving transformations $(T_v)_{v\in G}$. For any $\Lambda \subset E$ we consider the random return time $\tau$ at which $T_{S(\tau)}\in\Lambda$. We show that the corresponding induced skew product transformation is K-mixing whenever a natural subgroup of $G$ acts ergodically on $E$.

Limit set trichotomy and dichotomy for skew-product semiflows with applications

2009 ◽  
Vol 71 (7-8) ◽  
pp. 2834-2839
Author(s):  
Bin-Guo Wang ◽  
Wan-Tong Li
Keyword(s):  
Limit Set ◽  
Skew Product ◽  
Limit Set Trichotomy

Parabolic invariant tori in quasi-periodically forced skew-product maps

2021 ◽  
Vol 277 ◽  
pp. 234-274
Author(s):  
Xinyu Guan ◽  
Jianguo Si ◽  
Wen Si
Keyword(s):  
Invariant Tori ◽  
Skew Product ◽  
Product Maps

A skew-product which is Bernoulli

1978 ◽  
Vol 86 (2) ◽  
pp. 155-165 ◽  
Author(s):  
Paul C. Shields ◽  
Robert Burton
Keyword(s):  
Skew Product

Orbit equivalence and actions of

2006 ◽  
Vol 71 (1) ◽  
pp. 265-282 ◽  
Author(s):  
Asge Törnquist
Keyword(s):  
Probability Space ◽  
Free Groups ◽  
Orbit Equivalence ◽  
Borel Probability ◽  
Free Actions ◽  
Measure Preserving Transformations

AbstractIn this paper we show that there are “E0 many” orbit inequivalent free actions of the free groups , 2 ≤ n ≤ ∞ by measure preserving transformations on a standard Borel probability space. In particular, there are uncountably many such actions.

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