Complex continued fractions with restricted entries

Abstract

We study special infinite iterated function systems derived from complex continued fraction expansions with restricted entries. We focus our attention on the corresponding limit set whose Hausdorff dimension will be denoted by $h$. Our primary goal is to determine whether the $h$-dimensional Hausdorff and packing measure of the limit set is positive and finite.

Keywords

• iterated function systems
• complex continued fractions
• Hausdorff dimension
• Hausdorff measure
• packing measure.