非均匀双曲映射的几乎确定不变性原理中的速率

IF 2.2 1区 物理与天体物理 Q1 PHYSICS, MATHEMATICAL Communications in Mathematical Physics Pub Date : 2024-09-13 DOI:10.1007/s00220-024-05090-8
C. Cuny, J. Dedecker, A. Korepanov, F. Merlevède
{"title":"非均匀双曲映射的几乎确定不变性原理中的速率","authors":"C. Cuny,&nbsp;J. Dedecker,&nbsp;A. Korepanov,&nbsp;F. Merlevède","doi":"10.1007/s00220-024-05090-8","DOIUrl":null,"url":null,"abstract":"<div><p>We prove the almost sure invariance principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing invertible dynamical systems as Bunimovich flowers, billiards with flat points as in Chernov and Zhang (Stoch Dyn 5:535–553, 2005a, Nonlinearity 18:1527–1553, 2005b) and Wojtkowski’ (Commun Math Phys 126:507–533, 1990) system of two falling balls.For these examples, the ASIP is a new result, not covered by prior works for various reasons, notably because in absence of exponential contraction along stable leaves, it is challenging to employ the so-called Sinai’s trick (Sinai in Russ Math Surv 27:21–70, 1972; Bowen, Lecture Notes in Math vol. 470 (1975)) of reducing a nonuniformly hyperbolic system to a nonuniformly expanding one. Our strategy follows our previous papers on the ASIP for nonuniformly expanding maps, where we build a semiconjugacy to a specific renewal Markov shift and adapt the argument of Berkes et al. (Ann Probab 42:794–817, 2014). The main difference is that now the Markov shift is <i>two-sided</i>, the observables depend on the full trajectory, both the future and the past.</p></div>","PeriodicalId":522,"journal":{"name":"Communications in Mathematical Physics","volume":"405 10","pages":""},"PeriodicalIF":2.2000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://link.springer.com/content/pdf/10.1007/s00220-024-05090-8.pdf","citationCount":"0","resultStr":"{\"title\":\"Rates in Almost Sure Invariance Principle for Nonuniformly Hyperbolic Maps\",\"authors\":\"C. Cuny,&nbsp;J. Dedecker,&nbsp;A. Korepanov,&nbsp;F. Merlevède\",\"doi\":\"10.1007/s00220-024-05090-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>We prove the almost sure invariance principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing invertible dynamical systems as Bunimovich flowers, billiards with flat points as in Chernov and Zhang (Stoch Dyn 5:535–553, 2005a, Nonlinearity 18:1527–1553, 2005b) and Wojtkowski’ (Commun Math Phys 126:507–533, 1990) system of two falling balls.For these examples, the ASIP is a new result, not covered by prior works for various reasons, notably because in absence of exponential contraction along stable leaves, it is challenging to employ the so-called Sinai’s trick (Sinai in Russ Math Surv 27:21–70, 1972; Bowen, Lecture Notes in Math vol. 470 (1975)) of reducing a nonuniformly hyperbolic system to a nonuniformly expanding one. Our strategy follows our previous papers on the ASIP for nonuniformly expanding maps, where we build a semiconjugacy to a specific renewal Markov shift and adapt the argument of Berkes et al. (Ann Probab 42:794–817, 2014). The main difference is that now the Markov shift is <i>two-sided</i>, the observables depend on the full trajectory, both the future and the past.</p></div>\",\"PeriodicalId\":522,\"journal\":{\"name\":\"Communications in Mathematical Physics\",\"volume\":\"405 10\",\"pages\":\"\"},\"PeriodicalIF\":2.2000,\"publicationDate\":\"2024-09-13\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://link.springer.com/content/pdf/10.1007/s00220-024-05090-8.pdf\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Mathematical Physics\",\"FirstCategoryId\":\"101\",\"ListUrlMain\":\"https://link.springer.com/article/10.1007/s00220-024-05090-8\",\"RegionNum\":1,\"RegionCategory\":\"物理与天体物理\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"PHYSICS, MATHEMATICAL\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Mathematical Physics","FirstCategoryId":"101","ListUrlMain":"https://link.springer.com/article/10.1007/s00220-024-05090-8","RegionNum":1,"RegionCategory":"物理与天体物理","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"PHYSICS, MATHEMATICAL","Score":null,"Total":0}
引用次数: 0

摘要

我们以接近最优的误差率证明了非均匀双曲映射的几乎确定不变性原理(ASIP)。我们不假定沿稳定叶的指数收缩,因此我们的结果尤其涵盖了缓慢混合的可逆动力系统,如布尼莫维奇花、切尔诺夫和张 (Stoch Dyn 5:535-553, 2005a, Nonlinearity 18:1527-1553, 2005b) 中的带平点的台球,以及沃伊特科夫斯基 (Commun Math Phys 126:507-533, 1990) 的两落球系统。对于这些例子,ASIP 是一个新结果,由于种种原因而未被先前的工作所涵盖,主要是因为在没有沿稳定叶的指数收缩的情况下,采用所谓的西奈技巧(Sinai in Russ Math Surv 27:21-70, 1972; Bowen, Lecture Notes in Math vol. 470 (1975))将非均匀双曲系统还原为非均匀膨胀系统具有挑战性。我们的策略沿袭了我们之前关于非均匀扩展映射的 ASIP 的论文,在这些论文中,我们为特定的更新马尔可夫移动建立了一个半轭,并改编了 Berkes 等人(Ann Probab 42:794-817, 2014)的论证。主要区别在于现在的马尔可夫变换是双面的,观测值取决于整个轨迹,包括未来和过去。
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
分享 分享
微信好友 朋友圈 QQ好友 复制链接
本刊更多论文
Rates in Almost Sure Invariance Principle for Nonuniformly Hyperbolic Maps

We prove the almost sure invariance principle (ASIP) with close to optimal error rates for nonuniformly hyperbolic maps. We do not assume exponential contraction along stable leaves, therefore our result covers in particular slowly mixing invertible dynamical systems as Bunimovich flowers, billiards with flat points as in Chernov and Zhang (Stoch Dyn 5:535–553, 2005a, Nonlinearity 18:1527–1553, 2005b) and Wojtkowski’ (Commun Math Phys 126:507–533, 1990) system of two falling balls.For these examples, the ASIP is a new result, not covered by prior works for various reasons, notably because in absence of exponential contraction along stable leaves, it is challenging to employ the so-called Sinai’s trick (Sinai in Russ Math Surv 27:21–70, 1972; Bowen, Lecture Notes in Math vol. 470 (1975)) of reducing a nonuniformly hyperbolic system to a nonuniformly expanding one. Our strategy follows our previous papers on the ASIP for nonuniformly expanding maps, where we build a semiconjugacy to a specific renewal Markov shift and adapt the argument of Berkes et al. (Ann Probab 42:794–817, 2014). The main difference is that now the Markov shift is two-sided, the observables depend on the full trajectory, both the future and the past.

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
Communications in Mathematical Physics
Communications in Mathematical Physics 物理-物理:数学物理
CiteScore
4.70
自引率
8.30%
发文量
226
审稿时长
3-6 weeks
期刊介绍: The mission of Communications in Mathematical Physics is to offer a high forum for works which are motivated by the vision and the challenges of modern physics and which at the same time meet the highest mathematical standards.
期刊最新文献
Classification of Discrete Weak KAM Solutions on Linearly Repetitive Quasi-Periodic Sets Unravelling the Holomorphic Twist: Central Charges Spin-Bounded Correlations: Rotation Boxes Within and Beyond Quantum Theory Dynamics of the Collision of Two Nearly Equal Solitary Waves for the Zakharov–Kuznetsov Equation Emergence of Near-TAP Free Energy Functional in the SK Model at High Temperature
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
现在去查看 取消
×
提示
确定
0
微信
客服QQ
Book学术公众号 扫码关注我们
反馈
×
意见反馈
请填写您的意见或建议
请填写您的手机或邮箱
已复制链接
已复制链接
快去分享给好友吧!
我知道了
×
扫码分享
扫码分享
Book学术官方微信
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术
文献互助 智能选刊 最新文献 互助须知 联系我们:info@booksci.cn
Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。
Copyright © 2023 Book学术 All rights reserved.
ghs 京公网安备 11010802042870号 京ICP备2023020795号-1