立方体曲面上测地线的分布

IF 0.8 3区数学 Q2 MATHEMATICS

Mathematika Pub Date : 2023-02-11 DOI:10.1112/mtk.12188

Yuxuan Yang

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引用次数: 0

摘要

我们建立了一个Kronecker–Weyl型结果，关于自然不可积系统的时间定量等分布，即立方体表面上的测地流。我们的工具是Beck、Donders和Yang[Acta Math.Hungar.161（2020），66–184]以及Beck、Donders和Young[Acta数学.Hungar162（2020）、220–324]开发的短线祖先方法，以适当的方式进行了修改，以包含所有斜率。通过使用对称群S4的不可约表示，立方体的对称性进一步增强了该方法，这使得不规则指数的确定基本上更简单。

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The distribution of geodesics on the cube surface

We establish a Kronecker–Weyl type result, on time-quantitative equidistribution for a natural non-integrable system, geodesic flow on the cube surface. Our tool is the shortline-ancestor method developed in Beck, Donders, and Yang [Acta Math. Hungar. 161 (2020), 66–184] and Beck, Donders, and Yang [Acta Math. Hungar. 162 (2020), 220–324], modified in an appropriate way to embrace all slopes. The method is further enhanced by the symmetry of the cube through the use of the irreducible representations of the symmetric group S₄ which makes the determination of the irregularity exponent substantially simpler.

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来源期刊

Mathematika MATHEMATICS, APPLIED-MATHEMATICS

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Mathematika publishes both pure and applied mathematical articles and has done so continuously since its founding by Harold Davenport in the 1950s. The traditional emphasis has been towards the purer side of mathematics but applied mathematics and articles addressing both aspects are equally welcome. The journal is published by the London Mathematical Society, on behalf of its owner University College London, and will continue to publish research papers of the highest mathematical quality.