Sebe, Gabriela Ileana On convergence rate in the Gauss-Kuzmin problem for grotesque continued fractions. (English) Zbl 1014.11047 Monatsh. Math. 133, No. 3, 241-254 (2001). 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. Reviewer: Karma Dajani (Utrecht) Cited in 13 Documents MSC: 11K50 Metric theory of continued fractions 28D05 Measure-preserving transformations Keywords:ergodicity; grotesque continued fractions; infinite-order-chain; random systems with complete connections Citations:Zbl 1013.11045 PDFBibTeX XMLCite \textit{G. I. Sebe}, Monatsh. Math. 133, No. 3, 241--254 (2001; Zbl 1014.11047) Full Text: DOI