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The distribution of certain sequences connected with the continued fraction. (English) Zbl 0588.10061
This paper is an application of the powerful method which uses a realization of the natural extension of continued fractions. This realization provides an easy way to determine the distribution of the sequence $$(T^ jx, q_{j-1}/q_ j).$$ From this the distributions of sequences like $$(q_ n | q_ nx-p_ n|,\quad q_{n+1} | q_{n+1}x-p_{n+1}|)$$ can be calculated explicitly.
Reviewer: F.Schweiger

##### MSC:
 11K16 Normal numbers, radix expansions, Pisot numbers, Salem numbers, good lattice points, etc. 28D05 Measure-preserving transformations