Abstract
Continued fractions w.r.t. a specified class of numbers is considered. The invariant measures of the corresponding transformations are identified connecting the continued fractions with geodesics on the upper half plane. A problem of convergence in distribution of sums of the coefficients of the continued fraction is also considered.
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Chakraborty, P.S., Dasgupta, A. Invariant Measure and a Limit Theorem for Some Generalized Gauss Maps. Journal of Theoretical Probability 17, 387–401 (2004). https://doi.org/10.1023/B:JOTP.0000020700.45630.5c
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DOI: https://doi.org/10.1023/B:JOTP.0000020700.45630.5c