Inhomogeneous Diophantine approximation on curves and Hausdorff dimension

被引：8
作者：
Badziahin, Dzmitry [1 ]
机构：
[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England
来源：
ADVANCES IN MATHEMATICS | 2010年 / 223卷 / 01期
基金：
英国工程与自然科学研究理事会;
关键词：
Diophantine approximation; Lebesgues measure; Hausdorff dimension; Non-degenerate curve; Khintchine theorem; PLANAR CURVES; THEOREM; CONVERGENCE;
D O I：
10.1016/j.aim.2009.08.005
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in R-n akin to the well established homogeneous theory. More specifically, the measure theoretic results obtained generalize the fundamental homogeneous theorems of R.C. Baker (1978) [2], Dodson, Dickinson (2000) [18] and Beresnevich, Bernik, Kleinbock, Margulis (2002) [8]. In the case of planar curves, the complete Hausdorff dimension theory is developed. (C) 2009 Elsevier Inc. All rights reserved.
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收藏
页码：329 / 351
页数：23
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