The three-dimensional Poincaré continued fraction algorithm
type: Item
instance of: scholarly article
title: The three-dimensional Poincaré continued fraction algorithm
zbMATH Open document ID: 0840.11030
DOI: 10.1007/BF02783221
author: Yanyan Li
published in: Israel Journal of Mathematics
publication date: 1995-08-14T00:00:00Z
review text: The author proves that for Lebesgue-almost every line in the three-dimensional Euclidean space, the Poincaré continued fraction algorithm determines a unique vertex. Furthermore, the algorithm is nonergodic, although the Gauss map, defined by the algorithm, has an attractor and is ergodic. Finally, it is shown that the Euclidean algorithm and the horocycle flow are orbit equivalent.
Mathematics Subject Classification ID: 11K50
Mathematics Subject Classification ID: 37A99
Mathematics Subject Classification ID: 11A05
zbMATH DE Number: 784926
zbMATH Keywords: Poincaré continued fraction algorithm
zbMATH Keywords: Gauss map
zbMATH Keywords: Euclidean algorithm
zbMATH Keywords: horocycle flow
reviewed by: Sophia L. Kalpazidou
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 784926