{"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":0,"journal":{"name":"","volume":null,"pages":null},"PeriodicalIF":0.0,"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\":0,\"journal\":{\"name\":\"\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0,\"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\":\"\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://onlinelibrary.wiley.com/doi/10.1112/topo.12279\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"","FirstCategoryId":"100","ListUrlMain":"https://onlinelibrary.wiley.com/doi/10.1112/topo.12279","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
A criterion for density of the isoperiodic leaves in rank one affine invariant orbifolds
We define on any affine invariant orbifold a foliation 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 when 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 .
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