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Summable orbits 可和轨道
IF 1.1 1区 数学
Journal of Modern Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jmd.2023017
Snir Ben Ovadia
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引用次数: 0
Noncommutative coboundary equations over integrable systems 可积系统上的非交换共边方程
1区 数学
Journal of Modern Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jmd.2023020
Rafael de la Llave, Maria Saprykina
{"title":"Noncommutative coboundary equations over integrable systems","authors":"Rafael de la Llave, Maria Saprykina","doi":"10.3934/jmd.2023020","DOIUrl":"https://doi.org/10.3934/jmd.2023020","url":null,"abstract":"We prove an analog of the Livshits theorem for real-analytic families of cocycles over an integrable system with values in a Banach algebra$ {{mathscr G}} $or a Lie group. Namely, we consider an integrable dynamical system$ f:{{mathscr M}} equiv{{mathbb T}}^d times [-1, 1]^dto {{mathscr M}} $,$ f(theta, I) = (theta + I, I) $, and a real-analytic family of cocycles$ eta_{varepsilon} : {{mathscr M}} to {{mathscr G}} $indexed by a complex parameter$ {varepsilon} $in an open ball$ {{mathscr E}}_rho subset {{mathbb C}} $. We show that if$ eta_{varepsilon} $is close to identity and has trivial periodic data, i.e.,for each periodic point$ p = f^n p $and each$ {varepsilon} in {{mathscr E}}_{rho} $, then there exists a real-analytic family of maps$ phi_{varepsilon}: {{mathscr M}} to {{mathscr G}} $satisfying the coboundary equation$   eta_{varepsilon}(theta, I) = (phi_{varepsilon}circ f(theta, I))^{-1} cdot phi_{varepsilon} (theta, I)    $for all$ (theta, I)in {{mathscr M}} $and$ {varepsilon} in {{mathscr E}}_{rho/2} $.We also show that if the coboundary equation above with an analytic left-hand side$ eta_{varepsilon} $has a solution in the sense of formal power series in$ {varepsilon} $, then it has an analytic solution.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136201898","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Circle homeomorphisms with breaks with no $boldsymbol{C^{2-nu}}$ conjugacy 不带$bold符号{C^{2-nu}}$共轭的带断点的圆同胚
1区 数学
Journal of Modern Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jmd.2023019
Nataliya Goncharuk, Konstantin Khanin, Yury Kudryashov
{"title":"Circle homeomorphisms with breaks with no $boldsymbol{C^{2-nu}}$ conjugacy","authors":"Nataliya Goncharuk, Konstantin Khanin, Yury Kudryashov","doi":"10.3934/jmd.2023019","DOIUrl":"https://doi.org/10.3934/jmd.2023019","url":null,"abstract":"The rigidity theory for circle homeomorphisms with breaks has been studied intensively in the last 20 years. It was proved [15, 21, 17, 19] that under mild conditions of the Diophantine type on the rotation number any two $C^{2+alpha}$ smooth circle homeomorphisms with a break point are $C^1$ smoothly conjugate to each other, provided that they have the same rotation number and the same size of the break. In this paper we prove that the conjugacy may not be $C^{2-nu}$ even if the maps are analytic outside of the break points. This result shows that the rigidity theory for maps with singularities is very different from the linearizable case of circle diffeomorphisms where conjugacy is arbitrarily smooth, or even analytic, for sufficiently smooth diffeomorphisms.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135651051","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Regularizations of pseudo-automorphisms with positive algebraic entropy 具有正代数熵的伪自同构的正则化
IF 1.1 1区 数学
Journal of Modern Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jmd.2023006
A. Kuznetsova
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引用次数: 1
The Brin Prize works of Tim Austin 蒂姆·奥斯汀的布林奖作品
1区 数学
Journal of Modern Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jmd.2023024
Jean-Paul Thouvenot
{"title":"The Brin Prize works of Tim Austin","authors":"Jean-Paul Thouvenot","doi":"10.3934/jmd.2023024","DOIUrl":"https://doi.org/10.3934/jmd.2023024","url":null,"abstract":"The mathematical activity of Tim Austin has been, since the very beginning, quite abundant and versatile. We will describe and comment on three of his results which were selected as most representative for the Brin Prize Award and which culminated in the proof of the weak Pinsker structure theorem.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135445010","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The 2021 Michael Brin Prize in Dynamical Systems 2021年迈克尔·布林动力系统奖
1区 数学
Journal of Modern Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jmd.2023023
None The Editors
{"title":"The 2021 Michael Brin Prize in Dynamical Systems","authors":"None The Editors","doi":"10.3934/jmd.2023023","DOIUrl":"https://doi.org/10.3934/jmd.2023023","url":null,"abstract":"","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135445008","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Gate lattices and the stabilized automorphism group 门格与稳定自同构群
1区 数学
Journal of Modern Dynamics Pub Date : 2023-01-01 DOI: 10.3934/jmd.2023018
Ville Salo
{"title":"Gate lattices and the stabilized automorphism group","authors":"Ville Salo","doi":"10.3934/jmd.2023018","DOIUrl":"https://doi.org/10.3934/jmd.2023018","url":null,"abstract":"We study the stabilized automorphism group of a subshift of finite type with a certain gluing property called the eventual filling property, on a residually finite group $ G $. We show that the stabilized automorphism group is simply monolithic, i.e., it has a unique minimal non-trivial normal subgroup—the monolith—which is additionally simple. To describe the monolith, we introduce gate lattices, which apply (reversible logical) gates on finite-index subgroups of $ G $. The monolith is then precisely the commutator subgroup of the group generated by gate lattices. If the subshift and the group $ G $ have some additional properties, then the gate lattices generate a perfect group, thus they generate the monolith. In particular, this is always the case when the acting group is the integers. In this case we can also show that gate lattices generate the inert part of the stabilized automorphism group. Thus we obtain that the stabilized inert automorphism group of a one-dimensional mixing subshift of finite type is simple.","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135496193","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Some arithmetical aspects of renormalization in Teichmüller dynamics: On the occasion of Corinna Ulcigrai winning the Brin Prize teichmller动力学中重整化的一些算术方面:在Corinna Ulcigrai获得布林奖之际
IF 1.1 1区 数学
Journal of Modern Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jmd.2022006
S. Marmi
{"title":"Some arithmetical aspects of renormalization in Teichmüller dynamics: On the occasion of Corinna Ulcigrai winning the Brin Prize","authors":"S. Marmi","doi":"10.3934/jmd.2022006","DOIUrl":"https://doi.org/10.3934/jmd.2022006","url":null,"abstract":"<p style='text-indent:20px;'>We present some works of Corinna Ulcigrai closely related to Diophantine approximations and generalizing classical notions to the context of interval exchange maps, translation surfaces and Teichmüller dynamics.</p>","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70085079","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
The 2020 Michael Brin Prize in Dynamical Systems 2020年迈克尔·布林动力系统奖
IF 1.1 1区 数学
Journal of Modern Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jmd.2022004
The editors
{"title":"The 2020 Michael Brin Prize in Dynamical Systems","authors":"The editors","doi":"10.3934/jmd.2022004","DOIUrl":"https://doi.org/10.3934/jmd.2022004","url":null,"abstract":"<jats:p xml:lang=\"fr\" />","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70085411","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Urysohn-type theorem under a dynamical constraint: Non-compact case 动态约束下的urysohn型定理:非紧情况
IF 1.1 1区 数学
Journal of Modern Dynamics Pub Date : 2022-01-01 DOI: 10.3934/jmd.2022015
A. Fathi
{"title":"Urysohn-type theorem under a dynamical constraint: Non-compact case","authors":"A. Fathi","doi":"10.3934/jmd.2022015","DOIUrl":"https://doi.org/10.3934/jmd.2022015","url":null,"abstract":"","PeriodicalId":51087,"journal":{"name":"Journal of Modern Dynamics","volume":null,"pages":null},"PeriodicalIF":1.1,"publicationDate":"2022-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"70085214","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":1,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 1
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