On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field
type: Item
instance of: scholarly article
title: On ergodic theory of A. Schmidt's complex continued fractions over Gaussian field
zbMATH Open document ID: 0635.10042
DOI: 10.1007/BF01501166
author: Hitoshi Nakada
published in: Monatshefte für Mathematik
publication date: 1988-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178369
review text: We consider a transformation associated with \textit{A. L. Schmidt}'s complex continued fractions [ibid. 93, 39--62 (1982; Zbl 0467.10038)]. We discuss a relation between complex continued fractions and geodesics over a three dimensional hyperbolic space and give an absolutely continuous ergodic invariant measure for the transformation. As an application, we show some properties of complex continued fractions.
Mathematics Subject Classification ID: 11K50
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 30B70
zbMATH DE Number: 4033852
zbMATH Keywords: natural extension transformation
zbMATH Keywords: complex continued fractions
zbMATH Keywords: geodesics
zbMATH Keywords: invariant measure
MaRDI profile type: Publication
cites work: Q5515914
cites work: Q3669515
cites work: Fractions
cites work: Algorithms with mediant convergents and their metrical theory
cites work: Diophantine approximation of complex numbers
cites work: Ergodic theory for complex continued fractions
description: scientific article; zbMATH DE number 4033852