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Let T = [0, 1) be the additive group of real numbers modulo 1, α ∈ T be an irrational number and t ∈ T. We study ergodicity of skew product extensions T : T×Z → T×Z, T (x, s1, s2) = (x+α, s1 + 2χ[0,1/2)(x)− 1, s2 + 2χ[0,1/2)(x+ t)− 1).

Ergodicity of Z2extensions of irrational rotations

Ergodicity of Z²extensions of irrational rotations