Ergodicity of $\mathbb Z^2$ extensions of irrational rotations

Yuqing Zhang ¹

¹ ESI Boltzmanngasse 9 A-1090 Wien, Austria

Studia Mathematica, Tome 204 (2011) no. 3, pp. 235-246

Résumé

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 $T \colon \mathbb T\times \mathbb Z^2 \to \mathbb T\times \mathbb Z^2$, $T(x,s_1,s_2)=(x+\alpha,s_1+2\chi_{[0,{1}/{2})}(x)-1, s_2+2\chi_{[0,{1}/{2})}(x+t)-1)$.

Détail

DOI : 10.4064/sm204-3-3

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