论文标题
在曲线上赢得了差异很差的积分
Winning property of badly approximable points on curves
论文作者
论文摘要
在本文中，我们证明，在$ \ mathbb {r}^n $中的任何分析性非脱位曲线上都非常近似的点是绝对的获胜集。这证实了Badziahin和Velani（2014）所说的地区的一个关键猜想，这是Davenport问题从1960年代开始的深远概括。我们主要结果的各种后果之一是解决Bugeaud在实际数字上的问题的解决方案，而代数数量的任意程度非常近似。证明依赖于分形几何学和均匀动力学的新想法。
In this paper we prove that badly approximable points on any analytic non-degenerate curve in $\mathbb{R}^n$ is an absolute winning set. This confirms a key conjecture in the area stated by Badziahin and Velani (2014) which represents a far-reaching generalisation of Davenport's problem from the 1960s. Amongst various consequences of our main result is a solution to Bugeaud's problem on real numbers badly approximable by algebraic numbers of arbitrary degree. The proof relies on new ideas from fractal geometry and homogeneous dynamics.
