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Fukuyama, K.; Mori, S.; Tanabe, Y.
Acta Mathematica Hungarica, 06/2020, Volume: 161, Issue: 1Journal Article
For θ ∈ ( - ∞ , - 1 ) ∪ ( 1 , ∞ ) and for almost every x , it is known that the sequence { θ k x } is uniformly distributed modulo 1. The speed of convergence sensitively depends on the algebraic nature of θ . In this paper we prove that such dependence vanishes if we perturb the sequence by adding the irrational rotation { κ γ } . The speed becomes identical with that of the sequence of uniformly distributed independent random variables.
