论文标题
使用有效维度固定距离
Pinned Distance Sets Using Effective Dimension
论文作者
论文摘要
在本文中，我们使用算法工具，有效的维度和Kolmogorov的复杂性来研究距离集的分形维度。我们表明，对于任何分析集$ e \ subseteq \ r^2 $的hausdorff尺寸，严格大于一个，\ textit {dextiT {固定的距离集}的$ e $，$δ_xe $具有至少一个$ x $ x $ x $ x $ x $ x $ x的hausdorff维度。当$ e $的尺寸接近一个时，这会改善最著名的界限。
In this paper, we use algorithmic tools, effective dimension and Kolmogorov complexity, to study the fractal dimension of distance sets. We show that, for any analytic set $E\subseteq\R^2$ of Hausdorff dimension strictly greater than one, the \textit{pinned distance set} of $E$, $Δ_x E$, has Hausdorff dimension of at least $\frac{3}{4}$, for all points $x$ outside a set of Hausdorff dimension at most one. This improves the best known bounds when the dimension of $E$ is close to one.
