Sequences and dynamical systems associated with canonical approximation by rationals

2011/02/22 by Andrew Haas, Haas, Andrew
Mathematics · #11K60 #Dynamical Systems (math.DS) #FOS: Mathematics #Number Theory (math.NT) #math.DS #math.NT #msc:11K60

paper · pdf · doi:10.48550/arxiv.1102.4600

13 pages, 3 figures

arxiv created 2011/02/22 · arxiv updated 2011/02/23

Abstract

We study metrical properties of various subsequences associated to the sequence of rational approximants coming from the continued fraction of an irrational number. Our methods build upon Bosma, Jager and Wiedijk's proof of the Doblin-Lenstra conjecture as well as Jager's subsequent treatment of the sequence of approximation pairs.

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• Rational approximation with chosen numerators
• Rational approximations, multidimensional continued fractions and lattice reduction
• Rational Dynamical Systems
• Rational approximations of irrational numbers