Inhomogeneous Diophantine approximation on curves and Hausdorff dimension
Inhomogeneous Diophantine approximation on curves and Hausdorff dimension
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DOI：
10.1016/j.aim.2009.08.005
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发表时间：
2008-09
影响因子：
1.7
通讯作者：
D. Badziahin
中科院分区：
文献类型：
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作者：
D. Badziahin
本文的目的是发展一个连贯的理论，非齐次丢番图逼近曲线在Rnakin建立齐次理论。更具体地说，所得到的测度论结果推广了R. C. Baker（1978）[2]，Dodson，Dickinson（2000）[18]和Beresnevich，Bernik，Kleinbock，Margulis（2002）[8]。在平面曲线的情况下，发展了完备的Hausdorff维数理论。
The goal of this paper is to develop a coherent theory for inhomogeneous Diophantine approximation on curves in Rnakin 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.