THE 3-DIMENSIONAL POINCARE CONTINUED-FRACTION ALGORITHM

被引：21
|
作者：
NOGUEIRA, A [1 ]
机构：
[1] FED UNIV RIO DE JANEIRO,INST MATEMAT,BR-21945970 RIO JANEIRO,BRAZIL
来源：
ISRAEL JOURNAL OF MATHEMATICS | 1995年 / 90卷 / 1-3期
关键词：
D O I：
10.1007/BF02783221
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
It is proved here that for Lebesgue-almost every line in the three-dimensional Euclidean space, the Poincare continued fraction algorithm fixes a vertex. Besides, the algorithm is nonergodic, although the Gauss map, defined by the algorithm, has an attractor and is ergodic. It is also shown that the Euclidean algorithm and the horocycle flow are orbit equivalent.
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页码：373 / 401
页数：29
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