{"title":"流上并环的渐近性态","authors":"M. Lipatov","doi":"10.1090/mosc/320","DOIUrl":null,"url":null,"abstract":"In 1968, V. I. Oseledets formulated the question of the convergence in Birkhoff’s theorem and in the multiplicative ergodic theorem for measurable cocycles over flows, under the condition of integrability at any fixed time. In 2016, A. M. Stepin and the author of this paper established convergence along subsets of density 1 on the time axis. Here we show that, moreover, convergence takes place modulo subsets of finite measure of the time axis.","PeriodicalId":37924,"journal":{"name":"Transactions of the Moscow Mathematical Society","volume":" ","pages":""},"PeriodicalIF":0.0000,"publicationDate":"2022-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The asymptotic behaviour of cocycles over flows\",\"authors\":\"M. Lipatov\",\"doi\":\"10.1090/mosc/320\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In 1968, V. I. Oseledets formulated the question of the convergence in Birkhoff’s theorem and in the multiplicative ergodic theorem for measurable cocycles over flows, under the condition of integrability at any fixed time. In 2016, A. M. Stepin and the author of this paper established convergence along subsets of density 1 on the time axis. Here we show that, moreover, convergence takes place modulo subsets of finite measure of the time axis.\",\"PeriodicalId\":37924,\"journal\":{\"name\":\"Transactions of the Moscow Mathematical Society\",\"volume\":\" \",\"pages\":\"\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-03-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Transactions of the Moscow Mathematical Society\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.1090/mosc/320\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Transactions of the Moscow Mathematical Society","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1090/mosc/320","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"Mathematics","Score":null,"Total":0}
引用次数: 0
摘要
1968年，V. I. Oseledets在任意固定时间可积条件下，给出了流上可测环的Birkhoff定理和乘法遍历定理的收敛性问题。2016年，A. M. Stepin和本文作者在时间轴上沿密度1的子集建立了收敛性。这里我们进一步证明，收敛发生于时间轴的有限测度的模子集。
In 1968, V. I. Oseledets formulated the question of the convergence in Birkhoff’s theorem and in the multiplicative ergodic theorem for measurable cocycles over flows, under the condition of integrability at any fixed time. In 2016, A. M. Stepin and the author of this paper established convergence along subsets of density 1 on the time axis. Here we show that, moreover, convergence takes place modulo subsets of finite measure of the time axis.
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