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On convergence rate in the Gauss-Kuzmin problem for grotesque continued fractions. (English) Zbl 1014.11047

Using the methods developed by M. Iosifescu for the regular continued fraction expansion [Rev. Roum. Math. Pures Appl. 42, 71-88 (1997; Zbl 1013.11045)], the author gives an infinite-order-chain representation of the sequence of incomplete quotients of the grotesque continued fractions, and uses this to give a Gauss-Kuzmin type theorem for this expansion. She also proves a Gauss-Kuzmin theorem for the natural extension of the grotesque continued fraction operator and gives an estimate of the rate of convergence.

MSC:

11K50 Metric theory of continued fractions
28D05 Measure-preserving transformations

Citations:

Zbl 1013.11045
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