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Israel Journal of Mathematics

, Volume 209, Issue 2, pp 803–823 | Cite as

The convergence of the generalised Selmer algorithm

  • Henk BruinEmail author
  • Robbert Fokkink
  • Cor Kraaikamp
Article

Abstract

Schweiger introduced the notion of a subtractive algorithm, to classify certain types of multidimensional continued fractions. We study the limit behaviour of one particular subtractive algorithm, which generalises a continued fraction algorithm that was originally proposed by Selmer. The algorithm that we study depends on two parameters a and b. We first find a Markov partition if ab. Using inducing techniques, we then prove the existence of an ergodic absolutely continuous invariant probability measure ab for the quality of the rational approximations for Lebesgue-typical multidimensional vectors.

Keywords

Probability Measure Group Theory Rational Approximation Continue Fraction Limit Behaviour 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Hebrew University of Jerusalem 2015

Authors and Affiliations

  1. 1.Faculty of MathematicsUniversity of ViennaViennaAustria
  2. 2.Institute of Applied MathematicsDelft University of TechnologyCD DelftThe Netherlands

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