Hanus, Paweł; Urbański, Mariusz

Complex continued fractions with restricted entries

Electron. J. Differ. Equ. 1998, Paper No. 27, 9 p. (1998)


Summary: 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.

Mathematics Subject Classification

58F23, 58F03, 58F12


iterated function systems, complex continued fractions, Hausdorff dimension, Hausdorff measure, packing measure