The M\"{o}bius transformation of continued fractions with bounded upper   and lower partial quotients
  Let $h$: $x\mapsto \frac{ax+b}{cx+d} $ be the nondegenerate M\"{o}bius transformation with integer entries. We get a bound of the continued fraction of $h(x)$ by the upper and lower bound of continued fraction of $x$, which extends a result of Stambul \cite{S2}. 
Wencai Liu
math.NT