Gauss-like Continued Fraction Systems and their Dimension Spectrum

Abstract

To the Gauss-like continued fraction expansions we associate a conformal iterated function system whose limit set is of Lebesgue measure equal to 1. We show that the Texan Conjecture holds; i.e. for every $t \in [0,1]$ there exists a subsystem whose limit set has Hausdorff dimension equal to $t$.