Algorithms with mediant convergents and their metrical theory
type: Item
instance of: scholarly article
title: Algorithms with mediant convergents and their metrical theory
zbMATH Open document ID: 0702.11046
author: Shunji Ito
published in: Osaka Journal of Mathematics
publication date: 1989-01-01T00:00:00Z
review text: The paper is devoted to the study of two transformations on the unit interval which generate sets of mediant convergents. The first transformation has been considered as an example of an ergodic transformation with \(\sigma\)-finite measure at various instances. The second transformation is a remarkable application of the jump transformation construction [\textit{F. Schweiger}, Isr. J. Math. 21, 308- 318 (1975; Zbl 0314.10037)]. This leads to a new proof of a theorem of \textit{P. Erdős} [Acta Arith. 5, 359-369 (1959; Zbl 0097.035)] on diophantine approximation.
Mathematics Subject Classification ID: 11K50
Mathematics Subject Classification ID: 11K60
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 4150297
zbMATH Keywords: mediant convergents
zbMATH Keywords: ergodic transformation
zbMATH Keywords: jump transformation
reviewed by: Fritz Schweiger
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4150297