Ergodic theory of continued fractions

  • Marius Iosifescu
  • Cor Kraaikamp
Part of the Mathematics and Its Applications book series (MAIA, volume 547)


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.


Ergodic Theory Natural Extension Hausdorff Dimension Continue Fraction Irrational Number 
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Copyright information

© Springer Science+Business Media Dordrecht 2002

Authors and Affiliations

  • Marius Iosifescu
    • 1
  • Cor Kraaikamp
    • 2
  1. 1.Centre for Math. Statistics “Gheorghe Mihoc”Romanian AcademyBucharestRomania
  2. 2.Delft University of Technology, ITS (CROSS)DelftThe Netherlands

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