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Joint partial equidistribution of Farey rays in negatively curved manifolds and trees 负弯曲流形和树中法雷射线的联合局部等分布
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2024-01-08 DOI: 10.1017/etds.2023.116
JOUNI PARKKONEN, FRÉDÉRIC PAULIN
{"title":"Joint partial equidistribution of Farey rays in negatively curved manifolds and trees","authors":"JOUNI PARKKONEN, FRÉDÉRIC PAULIN","doi":"10.1017/etds.2023.116","DOIUrl":"https://doi.org/10.1017/etds.2023.116","url":null,"abstract":"<p>We prove a joint partial equidistribution result for common perpendiculars with given density on equidistributing equidistant hypersurfaces, towards a measure supported on truncated stable leaves. We recover a result of Marklof on the joint partial equidistribution of Farey fractions at a given density, and give several analogous arithmetic applications, including in Bruhat–Tits trees.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139396993","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 44 issue 2 Cover and Front matter ETS 第 44 卷第 2 期封面和封底
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2024-01-08 DOI: 10.1017/etds.2023.79
{"title":"ETS volume 44 issue 2 Cover and Front matter","authors":"","doi":"10.1017/etds.2023.79","DOIUrl":"https://doi.org/10.1017/etds.2023.79","url":null,"abstract":"","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139380099","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
Slices of the Takagi function 高木函数切片
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-12-20 DOI: 10.1017/etds.2023.117
ROOPE ANTTILA, BALÁZS BÁRÁNY, ANTTI KÄENMÄKI
{"title":"Slices of the Takagi function","authors":"ROOPE ANTTILA, BALÁZS BÁRÁNY, ANTTI KÄENMÄKI","doi":"10.1017/etds.2023.117","DOIUrl":"https://doi.org/10.1017/etds.2023.117","url":null,"abstract":"<p>We show that the Hausdorff dimension of any slice of the graph of the Takagi function is bounded above by the Assouad dimension of the graph minus one, and that the bound is sharp. The result is deduced from a statement on more general self-affine sets, which is of independent interest. We also prove that Marstrand’s slicing theorem on the graph of the Takagi function extends to all slices if and only if the upper pointwise dimension of every projection of the length measure on the <span>x</span>-axis lifted to the graph is at least one.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138817777","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
Levy and Thurston obstructions of finite subdivision rules 利维和瑟斯顿对有限细分规则的阻碍
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-12-15 DOI: 10.1017/etds.2023.115
INSUNG PARK
{"title":"Levy and Thurston obstructions of finite subdivision rules","authors":"INSUNG PARK","doi":"10.1017/etds.2023.115","DOIUrl":"https://doi.org/10.1017/etds.2023.115","url":null,"abstract":"For a post-critically finite branched covering of the sphere that is a subdivision map of a finite subdivision rule, we define non-expanding spines which determine the existence of a Levy cycle in a non-exhaustive semi-decidable algorithm. Especially when a finite subdivision rule has polynomial growth of edge subdivisions, the algorithm terminates very quickly, and the existence of a Levy cycle is equivalent to the existence of a Thurston obstruction. To show the equivalence between Levy and Thurston obstructions, we generalize the arcs intersecting obstruction theorem by Pilgrim and Tan [Combining rational maps and controlling obstructions. <jats:italic>Ergod. Th. &amp; Dynam. Sys.</jats:italic>18(1) (1998), 221–245] to a graph intersecting obstruction theorem. As a corollary, we prove that for a pair of post-critically finite polynomials, if at least one polynomial has core entropy zero, then their mating has a Levy cycle if and only if the mating has a Thurston obstruction.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138688204","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
Bracket words along Hardy field sequences 沿着哈代字段序列用括号括起来的单词
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-12-14 DOI: 10.1017/etds.2023.112
JAKUB KONIECZNY, CLEMENS MÜLLNER
{"title":"Bracket words along Hardy field sequences","authors":"JAKUB KONIECZNY, CLEMENS MÜLLNER","doi":"10.1017/etds.2023.112","DOIUrl":"https://doi.org/10.1017/etds.2023.112","url":null,"abstract":"<p>We study bracket words, which are a far-reaching generalization of Sturmian words, along Hardy field sequences, which are a far-reaching generalization of Piatetski-Shapiro sequences <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231213132148445-0557:S0143385723001128:S0143385723001128_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$lfloor n^c rfloor $</span></span></img></span></span>. We show that sequences thus obtained are deterministic (that is, they have subexponential subword complexity) and satisfy Sarnak’s conjecture.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138629710","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
引用次数: 0
Random and mean Lyapunov exponents for 的随机和平均李亚普诺夫指数
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-12-11 DOI: 10.1017/etds.2023.106
DIEGO ARMENTANO, GAUTAM CHINTA, SIDDHARTHA SAHI, MICHAEL SHUB
{"title":"Random and mean Lyapunov exponents for","authors":"DIEGO ARMENTANO, GAUTAM CHINTA, SIDDHARTHA SAHI, MICHAEL SHUB","doi":"10.1017/etds.2023.106","DOIUrl":"https://doi.org/10.1017/etds.2023.106","url":null,"abstract":"<p>We consider orthogonally invariant probability measures on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231207140347424-0756:S0143385723001062:S0143385723001062_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$operatorname {mathrm {GL}}_n(mathbb {R})$</span></span></img></span></span> and compare the mean of the logs of the moduli of eigenvalues of the matrices with the Lyapunov exponents of random matrix products independently drawn with respect to the measure. We give a lower bound for the former in terms of the latter. The results are motivated by Dedieu and Shub [On random and mean exponents for unitarily invariant probability measures on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231207140347424-0756:S0143385723001062:S0143385723001062_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$operatorname {mathrm {GL}}_n(mathbb {C})$</span></span></img></span></span>. <span>Astérisque</span> <span>287</span> (2003), xvii, 1–18]. A novel feature of our treatment is the use of the theory of spherical polynomials in the proof of our main result.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138566110","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
Invariant measures for substitutions on countable alphabets 可数字母表上替换的不变度量
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-12-11 DOI: 10.1017/etds.2023.113
WEBERTY DOMINGOS, SÉBASTIEN FERENCZI, ALI MESSAOUDI, GLAUCO VALLE
{"title":"Invariant measures for substitutions on countable alphabets","authors":"WEBERTY DOMINGOS, SÉBASTIEN FERENCZI, ALI MESSAOUDI, GLAUCO VALLE","doi":"10.1017/etds.2023.113","DOIUrl":"https://doi.org/10.1017/etds.2023.113","url":null,"abstract":"<p>In this work, we study ergodic and dynamical properties of symbolic dynamical system associated to substitutions on an infinite countable alphabet. Specifically, we consider shift dynamical systems associated to irreducible substitutions which have well-established properties in the case of finite alphabets. Based on dynamical properties of a countable integer matrix related to the substitution, we obtain results on existence and uniqueness of shift invariant measures.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138566371","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 dynamical classification for crossed products of fiberwise essentially minimal zero-dimensional dynamical systems 纤维本质最小零维动力系统交叉积的动力学分类
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-12-11 DOI: 10.1017/etds.2023.104
PAUL HERSTEDT
{"title":"A dynamical classification for crossed products of fiberwise essentially minimal zero-dimensional dynamical systems","authors":"PAUL HERSTEDT","doi":"10.1017/etds.2023.104","DOIUrl":"https://doi.org/10.1017/etds.2023.104","url":null,"abstract":"<p>We prove that crossed products of fiberwise essentially minimal zero-dimensional dynamical systems, a class that includes systems in which all orbit closures are minimal, have isomorphic <span>K</span>-theory if and only if the dynamical systems are strong orbit equivalent. Under the additional assumption that the dynamical systems have no periodic points, this gives a classification theorem including isomorphism of the associated crossed product <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20231207142051786-0306:S0143385723001049:S0143385723001049_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$C^*$</span></span></img></span></span>-algebras as well. We additionally explore the <span>K</span>-theory of such crossed products and the Bratteli diagrams associated to the dynamical systems.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138566378","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
Equilibrium states for non-uniformly expanding skew products 非均匀扩展倾斜积的均衡状态
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-12-11 DOI: 10.1017/etds.2023.111
GREGORY HEMENWAY
{"title":"Equilibrium states for non-uniformly expanding skew products","authors":"GREGORY HEMENWAY","doi":"10.1017/etds.2023.111","DOIUrl":"https://doi.org/10.1017/etds.2023.111","url":null,"abstract":"<p>We study equilibrium states for a class of non-uniformly expanding skew products, and show how a family of fiberwise transfer operators can be used to define the conditional measures along fibers of the product. We prove that the pushforward of the equilibrium state onto the base of the product is itself an equilibrium state for a Hölder potential defined via these fiberwise transfer operators.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138566366","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 44 issue 1 Cover and Back matter ETS 第 44 卷第 1 期封面和封底资料
IF 0.9 3区 数学
Ergodic Theory and Dynamical Systems Pub Date : 2023-12-06 DOI: 10.1017/etds.2023.78
{"title":"ETS volume 44 issue 1 Cover and Back matter","authors":"","doi":"10.1017/etds.2023.78","DOIUrl":"https://doi.org/10.1017/etds.2023.78","url":null,"abstract":"","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2023-12-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138596693","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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