The convergence of the generalised Selmer algorithm
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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 a ≥ b. Using inducing techniques, we then prove the existence of an ergodic absolutely continuous invariant probability measure a ≥ b for the quality of the rational approximations for Lebesgue-typical multidimensional vectors.
KeywordsProbability Measure Group Theory Rational Approximation Continue Fraction Limit Behaviour
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- H. Bruin, Lebesgue ergodicity of a dissipative subtractive algorithm, in W. Bahsoun et al (eds), Ergodic Theory, Open Dynamics and Coherent Structures, Springer Proceedings in Mathematics & Statistics, 2014.Google Scholar
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