{"title":"外太空极限展开路径集","authors":"Mladen Bestvina, Radhika Gupta, Jing Tao","doi":"10.1017/s1474748023000488","DOIUrl":null,"url":null,"abstract":"We construct an unfolding path in Outer space which does not converge in the boundary, and instead it accumulates on the entire 1-simplex of projectivized length measures on a nongeometric arational <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S1474748023000488_inline1.png\" /> <jats:tex-math> ${\\mathbb R}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-tree <jats:italic>T</jats:italic>. We also show that <jats:italic>T</jats:italic> admits exactly two dual ergodic projective currents. This is the first nongeometric example of an arational tree that is neither uniquely ergodic nor uniquely ergometric.","PeriodicalId":50002,"journal":{"name":"Journal of the Institute of Mathematics of Jussieu","volume":"2 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2024-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"LIMIT SETS OF UNFOLDING PATHS IN OUTER SPACE\",\"authors\":\"Mladen Bestvina, Radhika Gupta, Jing Tao\",\"doi\":\"10.1017/s1474748023000488\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We construct an unfolding path in Outer space which does not converge in the boundary, and instead it accumulates on the entire 1-simplex of projectivized length measures on a nongeometric arational <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\" mime-subtype=\\\"png\\\" xlink:href=\\\"S1474748023000488_inline1.png\\\" /> <jats:tex-math> ${\\\\mathbb R}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-tree <jats:italic>T</jats:italic>. We also show that <jats:italic>T</jats:italic> admits exactly two dual ergodic projective currents. This is the first nongeometric example of an arational tree that is neither uniquely ergodic nor uniquely ergometric.\",\"PeriodicalId\":50002,\"journal\":{\"name\":\"Journal of the Institute of Mathematics of Jussieu\",\"volume\":\"2 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2024-02-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of the Institute of Mathematics of Jussieu\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1017/s1474748023000488\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of the Institute of Mathematics of Jussieu","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1017/s1474748023000488","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
我们在外域空间构造了一条展开路径，它不在边界收敛，而是在非几何有理 ${\mathbb R}$ 树 T 上投影长度度量的整个 1-simplex 上累积。这是第一个既不是唯一遍历也不是唯一遍历的非几何有理树的例子。
We construct an unfolding path in Outer space which does not converge in the boundary, and instead it accumulates on the entire 1-simplex of projectivized length measures on a nongeometric arational ${\mathbb R}$ -tree T. We also show that T admits exactly two dual ergodic projective currents. This is the first nongeometric example of an arational tree that is neither uniquely ergodic nor uniquely ergometric.
期刊介绍：
The Journal of the Institute of Mathematics of Jussieu publishes original research papers in any branch of pure mathematics; papers in logic and applied mathematics will also be considered, particularly when they have direct connections with pure mathematics. Its policy is to feature a wide variety of research areas and it welcomes the submission of papers from all parts of the world. Selection for publication is on the basis of reports from specialist referees commissioned by the Editors.
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