Abstract:A two-dimensional Gauss-Kuzmin theorem for N -continued fraction expansions is shown. More precisely, we obtain a Gauss-Kuzmin theorem related to the natural extension of the measure-theoretical dynamical system associated to these expansions. Then, using characteristic properties of the transition operator associated with the random system with complete connections underlying N -continued fractions on the Banach space of complex-valued functions of bounded variation, we derive explicit lower and upper bounds … Show more
We generalize the result of Wirsing on Gauss transformation to the generalized tranformation Tp(x) = { p x } for any positive integer p. We give an estimate for the generalized Gauss-Kuzmin-Wirsing constant.
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