Abstract
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.
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© 2002 Springer Science+Business Media Dordrecht
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Iosifescu, M., Kraaikamp, C. (2002). Ergodic theory of continued fractions. In: Metrical Theory of Continued Fractions. Mathematics and Its Applications, vol 547. Springer, Dordrecht. https://doi.org/10.1007/978-94-015-9940-5_4
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DOI: https://doi.org/10.1007/978-94-015-9940-5_4
Publisher Name: Springer, Dordrecht
Print ISBN: 978-90-481-6130-0
Online ISBN: 978-94-015-9940-5
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