Article ID Journal Published Year Pages File Type
5774752 Journal of Mathematical Analysis and Applications 2017 21 Pages PDF
Abstract
In this paper we consider continued fraction (CF) expansions on intervals different from [0,1]. For every x in such interval we find a CF expansion with a finite number of possible digits. Using the natural extension, the density of the invariant measure is obtained in a number of examples. In case this method does not work, a Gauss-Kuzmin-Lévy based approximation method is used. Convergence of this method follows from [32] but the speed of convergence remains unknown. For a lot of known densities the method gives a very good approximation in a low number of iterations. Finally, a subfamily of the N-expansions is studied. In particular, the entropy as a function of a parameter α is estimated for N=2 and N=36. Interesting behavior can be observed from numerical results.
Related Topics
Physical Sciences and Engineering Mathematics Analysis
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