On the Pyatetskii-Shapiro normality criterion for continued fractions (Q690575)

The aim of the present paper is to improve the results described by \textit{N. G. Moshchevitin} and the author [Math. Notes 73, No. 4, 539--550 (2003); translation from Mat. Zametki 73, No. 4, 577--589 (2003; Zbl 1173.37302)] regarding the Pyatetskii-Shapiro normality criterion. The author manages to obtain sharp analogues of that criterion for a dynamical system associated with continued fractions and for some other class of dynamical systems with finite initial tailing following the approach given by \textit{Y. Kifer} et al. [Isr. J. Math. 124, 61--76 (2001; Zbl 1015.11040)].