On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

Hitoshi Nakada, Rie Natsui

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8 Citations (Scopus)


We study the metrical theory of fibred systems, in particular, in the case of continued fraction mixing systems. We get the limit distribution of the largest value of a continued fraction mixing stationary stochastic process with infinite expectation and some related results. These are analogous to J. Galambos, W. Philipp, and H. G. Diamond-J. D. Vaaler theorems for the regular continued fractions. As an application, we see that these theorems hold for Jacobi-Petron algorithm.

Original languageEnglish
Pages (from-to)267-288
Number of pages22
JournalMonatshefte fur Mathematik
Issue number4
Publication statusPublished - 2003 Apr



  • Continued fraction mixing
  • Fibred system
  • Jacobi-Perron algorithm

ASJC Scopus subject areas

  • Mathematics(all)

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