An inhomogeneous wave equation and non-linear Diophantine approximation

被引：3

作者：

Beresnevich, V. ^{[1
]}

Dodson, M. M. ^{[1
]}

Kristensen, S. ^{[2
]}

Levesley, J. ^{[1
]}

机构：

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

[2] Univ Edinburgh, Sch Math, Edinburgh EH9 3JZ, Midlothian, Scotland

来源：

ADVANCES IN MATHEMATICS | 2008年 / 217卷 / 02期

基金：

英国工程与自然科学研究理事会;

关键词：

Diophantine approximation; Hausdorff dimension; wave equation; small denominators problem; Diophantine phenomena;

D O I：

10.1016/j.aim.2007.09.003

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

A non-linear Diophantine condition involving perfect squares and arising from an inhomogeneous wave equation on the torus guarantees the existence of a smooth solution. The exceptional set associated with the failure of the Diophantine condition and hence of the existence of a smooth solution is studied. Both the Lebesgue and Hausdorff measures of this set are obtained. (c) 2007 Elsevier Inc. All rights reserved.

引用

页码：740 / 760

页数：21

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