Gauss-like Continued Fraction Systems and their Dimension Spectrum
Andrei E. Ghenciu
Source: Real Anal. Exchange Volume 34, Number 1 (2008), 17-28.
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 $t$.
Primary Subjects: 37A45, 37C45
Keywords: Gauss-like continued fractions ; Hausdorff dimension ; dimension spectrum
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