The Möbius transformation of continued fractions with bounded upper and lower partial quotients

Authors: WENCAI LIU

Abstract: Let $h$: $x\mapsto \frac{ax+b}{cx+d} $ be the nondegenerate Möbius transformation with integer entries. We get a bound of the continued fraction of $h(x)$ by upper and lower bounds of the continued fraction of $x$.

Keywords: Möbius transformation, continued fraction expansion, partial quotient.

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