Abstract
Letϕ: [0, 1]→R have continuous derivativeon the closed interval [0, 1], ∫ 10 ϕ(x)dx=0, and letα be irrational. Ifϕ(1) ≠ϕ(0), then (x, y) ↦ (x + α, y + ϕ (x)) is ergodic onR/Z ×R.
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Hellekalek, P., Larcher, G. On the ergodicity of a class of skew products. Israel J. Math. 54, 301–306 (1986). https://doi.org/10.1007/BF02764958
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DOI: https://doi.org/10.1007/BF02764958