On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field

Hitoshi Nakada

Research output: Contribution to journalArticle

7 Citations (Scopus)

Abstract

We construct a natural extension transformation associated with A. Schmidt's complex continued fractions. The transformation is defined on a subset of geodesics over a three dimensional hyperbolic space and an invariant measure for it is naturally induced from the hyperbolic measure. We discuss some applications of it to the metrical theory of continued fractions.

Original languageEnglish
Pages (from-to)131-150
Number of pages20
JournalMonatshefte für Mathematik
Volume105
Issue number2
DOIs
Publication statusPublished - 1988 Jun

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Compound or complex fraction
Gaussian Fields
Ergodic Theory
Continued fraction
Hyperbolic Space
Natural Extension
Invariant Measure
Geodesic
Three-dimensional
Subset

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field. / Nakada, Hitoshi.

In: Monatshefte für Mathematik, Vol. 105, No. 2, 06.1988, p. 131-150.

Research output: Contribution to journalArticle

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