数的遍历理论（影印版）

样章

作者：

Karma Dajani，Cor Kraaikamp 著

定价：

99.00元

版面字数：

330.00千字

开本：

16开

装帧形式：

精装

版次：

最新版次
印刷时间：

2026-01-06

ISBN：

978-7-04-065969-6

物料号：

65969-00

出版时间：

2026-03-27

读者对象：

学术著作

一级分类：

自然科学

二级分类：

数学与统计

三级分类：

数论

暂无

前辅文
Preface
1 Introduction
- 1.1 Decimal expansions of rational numbers
- 1.2 Another look at the decimal expansion
- 1.3 Continued fractions
- 1.4 For further reading
2 Variations on a theme (Other expansions)
- 2.1 n-ary expansions
- 2.2 Lüroth series
- 2.3 Generalized Lüroth series
- 2.4 β-expansions
3 Ergodicity
- 3.1 The Ergodic Theorem
- 3.2 Examples of normal numbers
- 3.3 β-transformations
- 3.4 Ergodic properties of the β-expansion
- 3.5 Ergodic properties of continued fractions Systems obtained from other systems
4 Systems obtained from other systems
- 4.1 GLS-expansion and β-expansion: A first glimpse at their connection
- 4.2 Induced and integral transformations
- 4.3 Natural extensions
- 4.4 Natural extension of the GLS transformation
- 4.5 Natural extension of the β-transformation
- 4.6 For further reading
5 Diophantine approximation and continued fractions
- 5.1 Introduction
- 5.2 The natural extension of the regular continued fraction
- 5.3 Approximation coefficients revisited
- 5.4 Other continued fractions
- 5.5 A skew product related to continued fractions
- 5.6 For further reading
6 Entropy
- 6.1 Introduction
- 6.2 The Shannon-McMillan-Breiman Theorem and some consequences
- 6.3 Saleski's Theorem
- 6.4 For further reading
Bibliography
Index