Ergodicity of Z Extensions of Irrational Rotations
نویسندگان
چکیده
Let T = [0, 1) be the additive group of real numbers modulo 1, α ∈ T be an irrational number and t ∈ T. We consider skew product extensions of irrational rotations by Z 2 determined by T : T × Z 2 → T × Z 2 T (x, s 1 , s 2) = " x + α, s 1 + 2χ [0, 1 2) (x) − 1, s 2 + 2χ [0, 1 2) (x + t) − 1 «. We study ergodic components of such extensions and use the results to display irregularities in the uniform distribution of the sequence Zα.
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