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 M$\operatorname{\ddot{o}}$bius transformations which carry the end points of the unit interval to zero and infinity, extending the classical regular and backwards continued fractions expansions. 
Avraham Bourla
math.NT math.DS