Ergodicity of $\mathbb Z^2$ extensions of irrational rotations
Volume 204 / 2011
Studia Mathematica 204 (2011), 235-246
MSC: Primary 37A25; Secondary 11A55.
DOI: 10.4064/sm204-3-3
Abstract
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 $T \colon \mathbb T\times \mathbb Z^2 \to \mathbb T\times \mathbb Z^2$, $T(x,s_1,s_2)=(x+\alpha,s_1+2\chi_{[0,{1}/{2})}(x)-1, s_2+2\chi_{[0,{1}/{2})}(x+t)-1)$.
