Slices of the Takagi function

IF 0.8 3区数学 Q2 MATHEMATICS

Ergodic Theory and Dynamical Systems Pub Date : 2023-12-20 DOI:10.1017/etds.2023.117

ROOPE ANTTILA, BALÁZS BÁRÁNY, ANTTI KÄENMÄKI

引用次数: 0

Abstract

We show that the Hausdorff dimension of any slice of the graph of the Takagi function is bounded above by the Assouad dimension of the graph minus one, and that the bound is sharp. The result is deduced from a statement on more general self-affine sets, which is of independent interest. We also prove that Marstrand’s slicing theorem on the graph of the Takagi function extends to all slices if and only if the upper pointwise dimension of every projection of the length measure on the x-axis lifted to the graph is at least one.

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高木函数切片

我们证明，高木函数图的任何切片的豪斯多夫维度都受图的阿苏阿德维度减一的约束，而且这个约束是尖锐的。这个结果是从一个关于更一般的自阿芬集合的声明中推导出来的，这也是我们的兴趣所在。我们还证明了马斯特兰关于高木函数图的切片定理扩展到所有切片，当且仅当长度度量在 x 轴上的每一个投影抬升到图的上点维度至少为一。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Ergodic Theory and Dynamical Systems 数学-数学

CiteScore

1.70

自引率

11.10%

发文量

113

审稿时长

6-12 weeks

期刊介绍： Ergodic Theory and Dynamical Systems focuses on a rich variety of research areas which, although diverse, employ as common themes global dynamical methods. The journal provides a focus for this important and flourishing area of mathematics and brings together many major contributions in the field. The journal acts as a forum for central problems of dynamical systems and of interactions of dynamical systems with areas such as differential geometry, number theory, operator algebras, celestial and statistical mechanics, and biology.