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

Volume 204 / 2011

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

Authors

  • Yuqing ZhangESI
    Boltzmanngasse 9
    A-1090 Wien, Austria
    e-mail

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