一阶仿射不变轨道中等周期叶密度的一个判据

IF 0.8 2区数学 Q2 MATHEMATICS Journal of Topology Pub Date : 2022-12-28 DOI:10.1112/topo.12279

Florent Ygouf

{"title":"一阶仿射不变轨道中等周期叶密度的一个判据","authors":"Florent Ygouf","doi":"10.1112/topo.12279","DOIUrl":null,"url":null,"abstract":"<p>We define on any affine invariant orbifold <math>\n <semantics>\n <mi>M</mi>\n <annotation>$\\mathcal {M}$</annotation>\n </semantics></math> a foliation <math>\n <semantics>\n <msup>\n <mi>F</mi>\n <mi>M</mi>\n </msup>\n <annotation>$\\mathcal {F}^{\\mathcal {M}}$</annotation>\n </semantics></math> that generalizes the isoperiodic foliation on strata of the moduli space of translation surfaces and study the dynamics of its leaves in the rank 1 case. We establish a criterion that ensures the density of the leaves and provide two applications of this criterion. The first one is a classification of the dynamical behavior of the leaves of <math>\n <semantics>\n <msup>\n <mi>F</mi>\n <mi>M</mi>\n </msup>\n <annotation>$\\mathcal {F}^{\\mathcal {M}}$</annotation>\n </semantics></math> when <math>\n <semantics>\n <mi>M</mi>\n <annotation>$\\mathcal {M}$</annotation>\n </semantics></math> is a connected component of a Prym eigenform locus in genus 2 or 3 and the second provides the first examples of dense isoperiodic leaves in the stratum <math>\n <semantics>\n <mrow>\n <mi>H</mi>\n <mo>(</mo>\n <mn>2</mn>\n <mo>,</mo>\n <mn>1</mn>\n <mo>,</mo>\n <mn>1</mn>\n <mo>)</mo>\n </mrow>\n <annotation>$\\mathcal {H}(2,1,1)$</annotation>\n </semantics></math>.</p>","PeriodicalId":56114,"journal":{"name":"Journal of Topology","volume":"16 1","pages":"1-19"},"PeriodicalIF":0.8000,"publicationDate":"2022-12-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12279","citationCount":"1","resultStr":"{\"title\":\"A criterion for density of the isoperiodic leaves in rank one affine invariant orbifolds\",\"authors\":\"Florent Ygouf\",\"doi\":\"10.1112/topo.12279\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>We define on any affine invariant orbifold <math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$\\\\mathcal {M}$</annotation>\\n </semantics></math> a foliation <math>\\n <semantics>\\n <msup>\\n <mi>F</mi>\\n <mi>M</mi>\\n </msup>\\n <annotation>$\\\\mathcal {F}^{\\\\mathcal {M}}$</annotation>\\n </semantics></math> that generalizes the isoperiodic foliation on strata of the moduli space of translation surfaces and study the dynamics of its leaves in the rank 1 case. We establish a criterion that ensures the density of the leaves and provide two applications of this criterion. The first one is a classification of the dynamical behavior of the leaves of <math>\\n <semantics>\\n <msup>\\n <mi>F</mi>\\n <mi>M</mi>\\n </msup>\\n <annotation>$\\\\mathcal {F}^{\\\\mathcal {M}}$</annotation>\\n </semantics></math> when <math>\\n <semantics>\\n <mi>M</mi>\\n <annotation>$\\\\mathcal {M}$</annotation>\\n </semantics></math> is a connected component of a Prym eigenform locus in genus 2 or 3 and the second provides the first examples of dense isoperiodic leaves in the stratum <math>\\n <semantics>\\n <mrow>\\n <mi>H</mi>\\n <mo>(</mo>\\n <mn>2</mn>\\n <mo>,</mo>\\n <mn>1</mn>\\n <mo>,</mo>\\n <mn>1</mn>\\n <mo>)</mo>\\n </mrow>\\n <annotation>$\\\\mathcal {H}(2,1,1)$</annotation>\\n </semantics></math>.</p>\",\"PeriodicalId\":56114,\"journal\":{\"name\":\"Journal of Topology\",\"volume\":\"16 1\",\"pages\":\"1-19\"},\"PeriodicalIF\":0.8000,\"publicationDate\":\"2022-12-28\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://onlinelibrary.wiley.com/doi/epdf/10.1112/topo.12279\",\"citationCount\":\"1\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Topology\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12279\",\"RegionNum\":2,\"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":"Journal of Topology","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12279","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS","Score":null,"Total":0}

引用次数: 1

摘要

我们在任何仿射不变的orbifold M$\mathcal｛M｝$上定义了一个叶理FM$\math cal｛F｝^｛\mathcal｝｝$，它推广了平移面的模空间的层上的等周期叶理，并且对1级叶片的动态特性进行了研究。我们建立了一个确保叶片密度的标准，并提供了该标准的两个应用。第一个是当M$\mathcal｛M｝$是亏格2或3中Prym本征型轨迹的连通分量并且第二个例子提供了层H（2，1，1）$\mathcal｛H｝（2，1,1）$中稠密等周期叶的第一个例子。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

摘要图片

查看原文

微信好友朋友圈 QQ好友复制链接

本刊更多论文

A criterion for density of the isoperiodic leaves in rank one affine invariant orbifolds

We define on any affine invariant orbifold $M$ a foliation $F^{M}$ that generalizes the isoperiodic foliation on strata of the moduli space of translation surfaces and study the dynamics of its leaves in the rank 1 case. We establish a criterion that ensures the density of the leaves and provide two applications of this criterion. The first one is a classification of the dynamical behavior of the leaves of $F^{M}$ when $M$ is a connected component of a Prym eigenform locus in genus 2 or 3 and the second provides the first examples of dense isoperiodic leaves in the stratum $H (2, 1, 1)$ .

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

来源期刊

Journal of Topology 数学-数学

CiteScore

2.00

自引率

9.10%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Topology publishes papers of high quality and significance in topology, geometry and adjacent areas of mathematics. Interesting, important and often unexpected links connect topology and geometry with many other parts of mathematics, and the editors welcome submissions on exciting new advances concerning such links, as well as those in the core subject areas of the journal. The Journal of Topology was founded in 2008. It is published quarterly with articles published individually online prior to appearing in a printed issue.