{"title":"立方体曲面上测地线的分布","authors":"Yuxuan Yang","doi":"10.1112/mtk.12188","DOIUrl":null,"url":null,"abstract":"<p>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. <b>161</b> (2020), 66–184] and Beck, Donders, and Yang [Acta Math. Hungar. <i>162</i> (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 <i>S</i><sub>4</sub> which makes the determination of the irregularity exponent substantially simpler.</p>","PeriodicalId":18463,"journal":{"name":"Mathematika","volume":null,"pages":null},"PeriodicalIF":0.8000,"publicationDate":"2023-02-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The distribution of geodesics on the cube surface\",\"authors\":\"Yuxuan Yang\",\"doi\":\"10.1112/mtk.12188\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>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. <b>161</b> (2020), 66–184] and Beck, Donders, and Yang [Acta Math. Hungar. <i>162</i> (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 <i>S</i><sub>4</sub> which makes the determination of the irregularity exponent substantially simpler.</p>\",\"PeriodicalId\":18463,\"journal\":{\"name\":\"Mathematika\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2023-02-11\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Mathematika\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12188\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematika","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/mtk.12188","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}
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.
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.
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