A generalization of a theorem of Lekkerkerker to Ostrowski's decomposition of natural numbers
Arithmetic diophantine approximation for continued fractions-like maps on the interval
We establish arithmetical properties and provide essential bounds for bi-sequences of approximation coefficients associated with the natural extension of maps, leading to continued fraction-like expansions. These maps are realized as the fractional part of Möbius transformations which carry the end points of the unit interval to zero and infinity, extending the classical regular and backwards continued fraction expansions.