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)

Abstract

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
Volume138
Issue number4
DOIs
Publication statusPublished - 2003 Apr

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Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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