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<p>A review of the metric theory of Rényi-type continued fraction expansions discussed in Lascu and Sebe (Acta Math Hungar 160, 292–313, 2020; Lascu and Sebe (Acta Arith 193: 283–292, 2020); Sebe and Lascu (Period Math Hung, 2020); Sebe and Lascu (Period Math Hung 85(2): 380–398, 2022) is given. These expansions represent a distinct class of backward continued fractions and were introduced by Göchenig and Haas (Ergodic Theory Dyn Syst 16:1241–1274, 1996). We briefly show the solutions of the Gauss–Kuzmin-type problem using various methods. The Borel–Berstein-type theorem is also given for these expansions.</p>

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Exploring Gauss–Kuzmin-type problems and a variant of the Borel–Bernstein theorem for Rényi-type continued fraction expansions

  • 期刊论文

  • 发表日期：

    2025年10月29日

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  • Dan Lascu,
  • Gabriela Ileana Sebe

摘要

A review of the metric theory of Rényi-type continued fraction expansions discussed in Lascu and Sebe (Acta Math Hungar 160, 292–313, 2020; Lascu and Sebe (Acta Arith 193: 283–292, 2020); Sebe and Lascu (Period Math Hung, 2020); Sebe and Lascu (Period Math Hung 85(2): 380–398, 2022) is given. These expansions represent a distinct class of backward continued fractions and were introduced by Göchenig and Haas (Ergodic Theory Dyn Syst 16:1241–1274, 1996). We briefly show the solutions of the Gauss–Kuzmin-type problem using various methods. The Borel–Berstein-type theorem is also given for these expansions.