### 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 language | English |
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Pages (from-to) | 267-288 |

Number of pages | 22 |

Journal | Monatshefte fur Mathematik |

Volume | 138 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2003 Apr |

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### Keywords

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

### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Monatshefte fur Mathematik*,

*138*(4), 267-288. https://doi.org/10.1007/s00605-002-0473-4

**On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm.** / Nakada, Hitoshi; Natsui, Rie.

Research output: Contribution to journal › Article

*Monatshefte fur Mathematik*, vol. 138, no. 4, pp. 267-288. https://doi.org/10.1007/s00605-002-0473-4

}

TY - JOUR

T1 - On the Metrical Theory of Continued Fraction Mixing Fibred Systems and Its Application to Jacobi-Perron Algorithm

AU - Nakada, Hitoshi

AU - Natsui, Rie

PY - 2003/4

Y1 - 2003/4

N2 - 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.

AB - 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.

KW - Continued fraction mixing

KW - Fibred system

KW - Jacobi-Perron algorithm

UR - http://www.scopus.com/inward/record.url?scp=0345060509&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0345060509&partnerID=8YFLogxK

U2 - 10.1007/s00605-002-0473-4

DO - 10.1007/s00605-002-0473-4

M3 - Article

AN - SCOPUS:0345060509

VL - 138

SP - 267

EP - 288

JO - Monatshefte fur Mathematik

JF - Monatshefte fur Mathematik

SN - 0026-9255

IS - 4

ER -