Ergodicity of $\mathbb Z^2$ extensions of irrational rotations
Studia Mathematica, Tome 204 (2011) no. 3, pp. 235-246
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
Let $\mathbb T=[0,1)$ be the additive group of real numbers
modulo $1$, $\alpha \in \mathbb T$ be an irrational number and
$t \in \mathbb T$.
We study ergodicity of skew product extensions
$T \colon \mathbb T\times \mathbb Z^2 \to \mathbb T\times \mathbb Z^2$,
$T(x,s_1,s_2)=(x+\alpha,s_1+2\chi_{[0,{1}/{2})}(x)-1,
s_2+2\chi_{[0,{1}/{2})}(x+t)-1)$.
Keywords:
mathbb additive group real numbers modulo alpha mathbb irrational number mathbb study ergodicity skew product extensions colon mathbb times mathbb mathbb times mathbb alpha chi chi
Affiliations des auteurs :
Yuqing Zhang 1
@article{10_4064_sm204_3_3,
author = {Yuqing Zhang},
title = {Ergodicity of $\mathbb Z^2$ extensions of irrational rotations},
journal = {Studia Mathematica},
pages = {235--246},
publisher = {mathdoc},
volume = {204},
number = {3},
year = {2011},
doi = {10.4064/sm204-3-3},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm204-3-3/}
}
Yuqing Zhang. Ergodicity of $\mathbb Z^2$ extensions of irrational rotations. Studia Mathematica, Tome 204 (2011) no. 3, pp. 235-246. doi: 10.4064/sm204-3-3
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