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

Hitoshi Nakada

doi:10.1007/BF01501166

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

Hitoshi Nakada

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 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 language	English
Pages (from-to)	131-150
Number of pages	20
Journal	Monatshefte für Mathematik
Volume	105
Issue number	2
DOIs	https://doi.org/10.1007/BF01501166
Publication status	Published - 1988 Jun 1

ASJC Scopus subject areas

Mathematics(all)

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

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