Continued fractions and the Markoff tree

被引：31

作者：

Bombieri, Enrico ^{[1
]}

机构：

[1] Inst Adv Study, Princeton, NJ 08540 USA

来源：

EXPOSITIONES MATHEMATICAE | 2007年 / 25卷 / 03期

关键词：

diophantine approximation; lagrange spectrum; continued fractions;

D O I：

10.1016/j.exmath.2006.10.002

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We give here a full account of Markoff's celebrated result on badly approximable numbers. The proofs rely exclusively on the classical theory of simple continued fractions, together with Harvey Cohn's method using words in the free group with two generators for the determination of the structure of periods of the continued fractions of Markov irrationals. Appendix A gives a short self-contained presentation of the results on continued fractions used here and Appendix B gives short proofs of some results on the still open uniqueness problem for Markoff numbers. (C) 2006 Elsevier GmbH. All rights reserved.

引用

页码：187 / 213

页数：27

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