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Conditional intermediate entropy and Birkhoff average properties of hyperbolic flows 双曲流的条件中间熵和Birkhoff平均性质
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-11-14 DOI: 10.1017/etds.2023.110
XIAOBO HOU, XUETING TIAN
{"title":"Conditional intermediate entropy and Birkhoff average properties of hyperbolic flows","authors":"XIAOBO HOU, XUETING TIAN","doi":"10.1017/etds.2023.110","DOIUrl":"https://doi.org/10.1017/etds.2023.110","url":null,"abstract":"Abstract Katok [Lyapunov exponents, entropy and periodic points of diffeomorphisms. Publ. Math. Inst. Hautes Études Sci. 51 (1980), 137–173] conjectured that every $C^{2}$ diffeomorphism f on a Riemannian manifold has the intermediate entropy property, that is, for any constant $c in [0, h_{mathrm {top}}(f))$ , there exists an ergodic measure $mu $ of f satisfying $h_{mu }(f)=c$ . In this paper, we obtain a conditional intermediate metric entropy property and two conditional intermediate Birkhoff average properties for basic sets of flows that characterize the refined roles of ergodic measures in the invariant ones. In this process, we establish a ‘multi-horseshoe’ entropy-dense property and use it to get the goal combined with conditional variational principles. We also obtain the same result for singular hyperbolic attractors.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"32 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"134954281","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: 1
Stabilized automorphism group of odometers and of Toeplitz subshifts 里程计和Toeplitz子位移的稳定自同构群
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-11-13 DOI: 10.1017/etds.2023.109
JENNIFER N. JONES-BARO
{"title":"Stabilized automorphism group of odometers and of Toeplitz subshifts","authors":"JENNIFER N. JONES-BARO","doi":"10.1017/etds.2023.109","DOIUrl":"https://doi.org/10.1017/etds.2023.109","url":null,"abstract":"Abstract We characterize the stabilized automorphism group for odometers and Toeplitz subshifts, and then prove an invariance property of the stabilized automorphism group of these dynamical systems. Namely, we prove the isomorphism invariance of the primes for which the p -adic valuation of the period structure tends to infinity. A particular case of interest is that for torsion-free odometers, the stabilized automorphism group is a full isomorphism invariant.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"27 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136346330","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: 1
Smooth models for certain fibered partially hyperbolic systems 某些纤维部分双曲系统的光滑模型
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-11-13 DOI: 10.1017/etds.2023.102
MEG DOUCETTE
{"title":"Smooth models for certain fibered partially hyperbolic systems","authors":"MEG DOUCETTE","doi":"10.1017/etds.2023.102","DOIUrl":"https://doi.org/10.1017/etds.2023.102","url":null,"abstract":"Abstract We prove that under restrictions on the fiber, any fibered partially hyperbolic system over a nilmanifold is leaf conjugate to a smooth model that is isometric on the fibers and descends to a hyperbolic nilmanifold automorphism on the base. One ingredient is a result of independent interest generalizing a result of Hiraide: an Anosov homeomorphism of a nilmanifold is topologically conjugate to a hyperbolic nilmanifold automorphism.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"12 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136347397","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: 3
Equidistribution of rational subspaces and their shapes 有理子空间的等分布及其形状
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-11-10 DOI: 10.1017/etds.2023.107
Menny Aka, Andrea Musso, Andreas Wieser
{"title":"Equidistribution of rational subspaces and their shapes","authors":"Menny Aka, Andrea Musso, Andreas Wieser","doi":"10.1017/etds.2023.107","DOIUrl":"https://doi.org/10.1017/etds.2023.107","url":null,"abstract":"Abstract To any k -dimensional subspace of $mathbb {Q}^n$ one can naturally associate a point in the Grassmannian $mathrm {Gr}_{n,k}(mathbb {R})$ and two shapes of lattices of rank k and $n-k$ , respectively. These lattices originate by intersecting the k -dimensional subspace and its orthogonal with the lattice $mathbb {Z}^n$ . Using unipotent dynamics, we prove simultaneous equidistribution of all of these objects under congruence conditions when $(k,n) neq (2,4)$ .","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"84 10","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087569","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: 4
ETS volume 43 issue 12 Cover and Back matter ETS第43卷第12期封面和封底
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-11-07 DOI: 10.1017/etds.2022.108
{"title":"ETS volume 43 issue 12 Cover and Back matter","authors":"","doi":"10.1017/etds.2022.108","DOIUrl":"https://doi.org/10.1017/etds.2022.108","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":"280 8","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135475220","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
Markov capacity for factor codes with an unambiguous symbol 具有明确符号的因子码的马尔可夫容量
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-11-07 DOI: 10.1017/etds.2023.103
GUANGYUE HAN, BRIAN MARCUS, CHENGYU WU
{"title":"Markov capacity for factor codes with an unambiguous symbol","authors":"GUANGYUE HAN, BRIAN MARCUS, CHENGYU WU","doi":"10.1017/etds.2023.103","DOIUrl":"https://doi.org/10.1017/etds.2023.103","url":null,"abstract":"Abstract In this paper, we first give a necessary and sufficient condition for a factor code with an unambiguous symbol to admit a subshift of finite type restricted to which it is one-to-one and onto. We then give a necessary and sufficient condition for the standard factor code on a spoke graph to admit a subshift of finite type restricted to which it is finite-to-one and onto. We also conjecture that for such a code, the finite-to-one and onto property is equivalent to the existence of a stationary Markov chain that achieves the capacity of the corresponding deterministic channel.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"29 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135475739","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 12 Cover and Front matter ETS第43卷第12期封面和封面问题
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-11-07 DOI: 10.1017/etds.2022.107
{"title":"ETS volume 43 issue 12 Cover and Front matter","authors":"","doi":"10.1017/etds.2022.107","DOIUrl":"https://doi.org/10.1017/etds.2022.107","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":"285 S5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135475348","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
A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class 从部分双曲链递推类中弹出马蹄形的机制
3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-11-03 DOI: 10.1017/etds.2023.76
Bonatti, Christian, Shinohara, Katsutoshi
{"title":"A mechanism for ejecting a horseshoe from a partially hyperbolic chain recurrence class","authors":"Bonatti, Christian, Shinohara, Katsutoshi","doi":"10.1017/etds.2023.76","DOIUrl":"https://doi.org/10.1017/etds.2023.76","url":null,"abstract":"Abstract We give a $C^1$ -perturbation technique for ejecting an a priori given finite set of periodic points preserving a given finite set of homo/heteroclinic intersections from a chain recurrence class of a periodic point. The technique is first stated under a simpler setting called a Markov iterated function system, a two-dimensional iterated function system in which the compositions are chosen in a Markovian way. Then we apply the result to the setting of three-dimensional partially hyperbolic diffeomorphisms.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"217 S696","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135775009","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: 1
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":"32 4","pages":"0"},"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":"14 3","pages":"0"},"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
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