A generalization of the Gauss map and some classical theorems on continued fractions

被引：7

作者：

Cruz, SD ^{[1
]}

da Rocha, LFC ^{[1
]}

机构：

[1] UFRGS, Inst Matemat, Belo Horizonte, MG, Brazil

来源：

NONLINEARITY | 2005年 / 18卷 / 02期

关键词：

D O I：

10.1088/0951-7715/18/2/003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this work we generalize the continued fraction algorithm to piecewise rotations of the circle and prove its ergodicity under a finite explicit measure. Using this algorithm, we generalize the classical results on the a.e. convergence of the arithmetic and geometric means of the partial quotients and the Khinchin-Levy theorem.

引用

页码：505 / 525

页数：21

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