Ergodic theory of continued fractions
In this chapter applications of the ergodic properties of the continued fraction transformation τ and its natural extension τ̄ are given. Next, two operations (‘singularization’ and ‘insertion’) on incomplete quotients are introduced, which allow to obtain most of the continued fraction expansions related to the RCF expansion. Ergodic properties of these expansions are also derived.
KeywordsErgodic Theory Natural Extension Hausdorff Dimension Continue Fraction Irrational Number
Unable to display preview. Download preview PDF.