发布求助
文献互助 智能选刊 最新文献

Ergodic Theory and Dynamical Systems最新文献

筛选
英文 中文
Geometrical representation of subshifts for primitive substitutions 原始替换的子移位的几何表示
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-11-03 DOI: 10.1017/etds.2023.101
PAUL MERCAT
{"title":"Geometrical representation of subshifts for primitive substitutions","authors":"PAUL MERCAT","doi":"10.1017/etds.2023.101","DOIUrl":"https://doi.org/10.1017/etds.2023.101","url":null,"abstract":"Abstract For any primitive substitution whose Perron eigenvalue is a Pisot unit, we construct a domain exchange that is measurably conjugate to the subshift. Additionally, we give a condition for the subshift to be a finite extension of a torus translation. For the particular case of weakly irreducible Pisot substitutions, we show that the subshift is either a finite extension of a torus translation or its eigenvalues are roots of unity. Furthermore, we provide an algorithm to compute eigenvalues of the subshift associated with any primitive pseudo-unimodular substitution.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135819334","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Distortion element in the automorphism group of a full shift 全移位自同构群中的畸变元
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-10-23 DOI: 10.1017/etds.2023.67
ANTONIN CALLARD, VILLE SALO
{"title":"Distortion element in the automorphism group of a full shift","authors":"ANTONIN CALLARD, VILLE SALO","doi":"10.1017/etds.2023.67","DOIUrl":"https://doi.org/10.1017/etds.2023.67","url":null,"abstract":"Abstract We show that there is a distortion element in a finitely generated subgroup G of the automorphism group of the full shift, namely an element of infinite order whose word norm grows polylogarithmically. As a corollary, we obtain a lower bound on the entropy dimension of any subshift containing a copy of G , and that a sofic shift’s automorphism group contains a distortion element if and only if the sofic shift is uncountable. We obtain also that groups of Turing machines and the higher-dimensional Brin–Thompson groups $mV$ admit distortion elements; in particular, $2V$ (unlike V ) does not admit a proper action on a CAT $(0)$ cube complex. In each case, the distortion element roughly corresponds to the SMART machine of Cassaigne, Ollinger, and Torres-Avilés [A small minimal aperiodic reversible Turing machine. J. Comput. System Sci. 84 (2017), 288–301].","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135405358","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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 measure rigidity and equidistribution results for β-maps 一些β-图的测量刚度和均匀分布结果
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-10-23 DOI: 10.1017/etds.2023.75
NEVO FISHBEIN
{"title":"Some measure rigidity and equidistribution results for <i>β</i>-maps","authors":"NEVO FISHBEIN","doi":"10.1017/etds.2023.75","DOIUrl":"https://doi.org/10.1017/etds.2023.75","url":null,"abstract":"Abstract We prove $times a times b$ measure rigidity for multiplicatively independent pairs when $ain mathbb {N}$ and $b&gt;1$ is a ‘specified’ real number (the b -expansion of $1$ has a tail or bounded runs of $0$ s) under a positive entropy condition. This is done by proving a mean decay of the Fourier series of the point masses average along $times b$ orbits. We also prove a quantitative version of this decay under stronger conditions on the $times a$ invariant measure. The quantitative version together with the $times b$ invariance of the limit measure is a step toward a general Host-type pointwise equidistribution theorem in which the equidistribution is for Parry measure instead of Lebesgue. We show that finite memory length measures on the a -shift meet the mentioned conditions for mean convergence. Our main proof relies on techniques of Hochman.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135411846","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
Katok’s special representation theorem for multidimensional Borel flows 多维波雷尔流的Katok特殊表示定理
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-10-23 DOI: 10.1017/etds.2023.62
KONSTANTIN SLUTSKY
{"title":"Katok’s special representation theorem for multidimensional Borel flows","authors":"KONSTANTIN SLUTSKY","doi":"10.1017/etds.2023.62","DOIUrl":"https://doi.org/10.1017/etds.2023.62","url":null,"abstract":"Abstract Katok’s special representation theorem states that any free ergodic measure- preserving $mathbb {R}^{d}$ -flow can be realized as a special flow over a $mathbb {Z}^{d}$ -action. It provides a multidimensional generalization of the ‘flow under a function’ construction. We prove the analog of Katok’s theorem in the framework of Borel dynamics and show that, likewise, all free Borel $mathbb {R}^{d}$ -flows emerge from $mathbb {Z}^{d}$ -actions through the special flow construction using bi-Lipschitz cocycles.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135405217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
On the ergodicity of unitary frame flows on Kähler manifolds Kähler流形上酉坐标系流的遍历性
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-10-16 DOI: 10.1017/etds.2023.72
MIHAJLO CEKIĆ, THIBAULT LEFEUVRE, ANDREI MOROIANU, UWE SEMMELMANN
{"title":"On the ergodicity of unitary frame flows on Kähler manifolds","authors":"MIHAJLO CEKIĆ, THIBAULT LEFEUVRE, ANDREI MOROIANU, UWE SEMMELMANN","doi":"10.1017/etds.2023.72","DOIUrl":"https://doi.org/10.1017/etds.2023.72","url":null,"abstract":"Abstract Let $(M,g,J)$ be a closed Kähler manifold with negative sectional curvature and complex dimension $m := dim _{mathbb {C}} M geq 2$ . In this article, we study the unitary frame flow , that is, the restriction of the frame flow to the principal $mathrm {U}(m)$ -bundle $F_{mathbb {C}}M$ of unitary frames. We show that if $m geq 6$ is even and $m neq 28$ , there exists $unicode{x3bb} (m) in (0, 1)$ such that if $(M, g)$ has negative $unicode{x3bb} (m)$ -pinched holomorphic sectional curvature, then the unitary frame flow is ergodic and mixing. The constants $unicode{x3bb} (m)$ satisfy $unicode{x3bb} (6) = 0.9330...$ , $lim _{m to +infty } unicode{x3bb} (m) = {11}/{12} = 0.9166...$ , and $m mapsto unicode{x3bb} (m)$ is decreasing. This extends to the even-dimensional case the results of Brin and Gromov [On the ergodicity of frame flows. Invent. Math. 60 (1) (1980), 1–7] who proved ergodicity of the unitary frame flow on negatively curved compact Kähler manifolds of odd complex dimension.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136113513","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 2
Statistical determinism in non-Lipschitz dynamical systems 非lipschitz动力系统中的统计决定论
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-10-11 DOI: 10.1017/etds.2023.74
Theodore D. Drivas, Alexei A. Mailybaev, Artem Raibekas
{"title":"Statistical determinism in non-Lipschitz dynamical systems","authors":"Theodore D. Drivas, Alexei A. Mailybaev, Artem Raibekas","doi":"10.1017/etds.2023.74","DOIUrl":"https://doi.org/10.1017/etds.2023.74","url":null,"abstract":"Abstract We study a class of ordinary differential equations with a non-Lipschitz point singularity that admits non-unique solutions through this point. As a selection criterion, we introduce stochastic regularizations depending on a parameter $nu $ : the regularized dynamics is globally defined for each $nu&gt; 0$ , and the original singular system is recovered in the limit of vanishing $nu $ . We prove that this limit yields a unique statistical solution independent of regularization when the deterministic system possesses a chaotic attractor having a physical measure with the convergence to equilibrium property. In this case, solutions become spontaneously stochastic after passing through the singularity: they are selected randomly with an intrinsic probability distribution.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136058223","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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: 8
Exponential multiple mixing for commuting automorphisms of a nilmanifold 零流形交换自同构的指数多重混合
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-10-11 DOI: 10.1017/etds.2023.73
TIMOTHÉE BÉNARD, PÉTER P. VARJÚ
{"title":"Exponential multiple mixing for commuting automorphisms of a nilmanifold","authors":"TIMOTHÉE BÉNARD, PÉTER P. VARJÚ","doi":"10.1017/etds.2023.73","DOIUrl":"https://doi.org/10.1017/etds.2023.73","url":null,"abstract":"Abstract Let $lin mathbb {N}_{ge 1}$ and $alpha : mathbb {Z}^lrightarrow text {Aut}(mathscr {N})$ be an action of $mathbb {Z}^l$ by automorphisms on a compact nilmanifold $mathscr{N}$ . We assume the action of every $alpha (z)$ is ergodic for $zin mathbb {Z}^lsmallsetminus {0}$ and show that $alpha $ satisfies exponential n -mixing for any integer $ngeq 2$ . This extends the results of Gorodnik and Spatzier [Mixing properties of commuting nilmanifold automorphisms. Acta Math. 215 (2015), 127–159].","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136211325","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
-chain closing lemma for certain partially hyperbolic diffeomorphisms 某些部分双曲微分同态的-链闭引理
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-10-11 DOI: 10.1017/etds.2023.71
YI SHI, XIAODONG WANG
{"title":"-chain closing lemma for certain partially hyperbolic diffeomorphisms","authors":"YI SHI, XIAODONG WANG","doi":"10.1017/etds.2023.71","DOIUrl":"https://doi.org/10.1017/etds.2023.71","url":null,"abstract":"Abstract For every $rin mathbb {N}_{geq 2}cup {infty }$ , we prove a $C^r$ -orbit connecting lemma for dynamically coherent and plaque expansive partially hyperbolic diffeomorphisms with one-dimensional orientation preserving center bundle. To be precise, for such a diffeomorphism f , if a point y is chain attainable from x through pseudo-orbits, then for any neighborhood U of x and any neighborhood V of y , there exist true orbits from U to V by arbitrarily $C^r$ -small perturbations. As a consequence, we prove that for $C^r$ -generic diffeomorphisms in this class, periodic points are dense in the chain recurrent set, and chain transitivity implies transitivity.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136211303","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
ETS volume 43 issue 11 Cover and Back matter ETS第43卷第11期封面和封底
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-10-05 DOI: 10.1017/etds.2022.106
{"title":"ETS volume 43 issue 11 Cover and Back matter","authors":"","doi":"10.1017/etds.2022.106","DOIUrl":"https://doi.org/10.1017/etds.2022.106","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135435850","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
ETS volume 43 issue 11 Cover and Front matter ETS第43卷第11期封面和封面问题
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-10-05 DOI: 10.1017/etds.2022.105
{"title":"ETS volume 43 issue 11 Cover and Front matter","authors":"","doi":"10.1017/etds.2022.105","DOIUrl":"https://doi.org/10.1017/etds.2022.105","url":null,"abstract":"An abstract is not available for this content so a preview has been provided. As you have access to this content, a full PDF is available via the ‘Save PDF’ action button.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-10-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135481175","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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
首页 上一页
0
×
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
请完成安全验证×
相关产品
×
本文献相关产品
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 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号：481959085
Book学术官方微信