Ergodic Theory and Dynamical Systems最新文献

{"title":"Non-concentration property of Patterson–Sullivan measures for Anosov subgroups","authors":"DONGRYUL M. KIM, HEE OH","doi":"10.1017/etds.2024.55","DOIUrl":"https://doi.org/10.1017/etds.2024.55","url":null,"abstract":"Let <jats:italic>G</jats:italic> be a connected semisimple real algebraic group. For a Zariski dense Anosov subgroup <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline1.png\"/> <jats:tex-math> $Gamma <G$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with respect to a parabolic subgroup <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline2.png\"/> <jats:tex-math> $P_theta $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, we prove that any <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline3.png\"/> <jats:tex-math> $Gamma $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-Patterson–Sullivan measure charges no mass on any proper subvariety of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline4.png\"/> <jats:tex-math> $G/P_theta $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. More generally, we prove that for a Zariski dense <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline5.png\"/> <jats:tex-math> $theta $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-transverse subgroup <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline6.png\"/> <jats:tex-math> $Gamma <G$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, any <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline7.png\"/> <jats:tex-math> $(Gamma , psi )$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-Patterson–Sullivan measure charges no mass on any proper subvariety of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline8.png\"/> <jats:tex-math> $G/P_theta $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, provided the <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline9.png\"/> <jats:tex-math> $psi $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-Poincaré series of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000555_inline10.png\"/> <jats:tex-math> $Gamma $ </jats:tex-math> </jats:alternatives> </jats:inlin","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142265586","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}

{"title":"Multifractal analysis of homological growth rates for hyperbolic surfaces","authors":"JOHANNES JAERISCH, HIROKI TAKAHASI","doi":"10.1017/etds.2024.62","DOIUrl":"https://doi.org/10.1017/etds.2024.62","url":null,"abstract":"We perform a multifractal analysis of homological growth rates of oriented geodesics on hyperbolic surfaces. Our main result provides a formula for the Hausdorff dimension of level sets of prescribed growth rates in terms of a generalized Poincaré exponent of the Fuchsian group. We employ symbolic dynamics developed by Bowen and Series, ergodic theory and thermodynamic formalism to prove the analyticity of the dimension spectrum.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142265587","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}

{"title":"Rigidity of flat holonomies","authors":"GÉRARD BESSON, GILLES COURTOIS, SA’AR HERSONSKY","doi":"10.1017/etds.2024.58","DOIUrl":"https://doi.org/10.1017/etds.2024.58","url":null,"abstract":"We prove that the existence of one horosphere in the universal cover of a closed Riemannian manifold of dimension <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000580_inline1.png\"/> <jats:tex-math> $n geq 3$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> with strongly <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000580_inline2.png\"/> <jats:tex-math> $1/4$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-pinched or relatively <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000580_inline3.png\"/> <jats:tex-math> $1/2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-pinched sectional curvature, on which the stable holonomy along one horosphere coincides with the Riemannian parallel transport, implies that the manifold is homothetic to a real hyperbolic manifold.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142265588","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}

{"title":"A recurrence-type strong Borel–Cantelli lemma for Axiom A diffeomorphisms","authors":"ALEJANDRO RODRIGUEZ SPONHEIMER","doi":"10.1017/etds.2024.64","DOIUrl":"https://doi.org/10.1017/etds.2024.64","url":null,"abstract":"Let <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000646_inline1.png\"/> <jats:tex-math> $(X,mu ,T,d)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> be a metric measure-preserving dynamical system such that three-fold correlations decay exponentially for Lipschitz continuous observables. Given a sequence <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000646_inline2.png\"/> <jats:tex-math> $(M_k)$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> that converges to <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000646_inline3.png\"/> <jats:tex-math> $0$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> slowly enough, we obtain a strong dynamical Borel–Cantelli result for recurrence, that is, for <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000646_inline4.png\"/> <jats:tex-math> $mu $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-almost every <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000646_inline5.png\"/> <jats:tex-math> $xin X$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:disp-formula> <jats:alternatives> <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000646_eqnu1.png\"/> <jats:tex-math> $$ begin{align*} lim_{n to infty}frac{sum_{k=1}^{n} mathbf{1}_{B_k(x)}(T^{k}x)} {sum_{k=1}^{n} mu(B_k(x))} = 1, end{align*} $$ </jats:tex-math> </jats:alternatives> </jats:disp-formula>where <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000646_inline6.png\"/> <jats:tex-math> $mu (B_k(x)) = M_k$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>. In particular, we show that this result holds for Axiom A diffeomorphisms and equilibrium states under certain assumptions.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142265499","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}

{"title":"On transversal Hölder regularity for flat Wieler solenoids","authors":"RODRIGO TREVIÑO","doi":"10.1017/etds.2024.41","DOIUrl":"https://doi.org/10.1017/etds.2024.41","url":null,"abstract":"This paper studies various aspects of inverse limits of locally expanding affine linear maps on flat branched manifolds, which I call flat Wieler solenoids. Among the aspects studied are different types of cohomologies, the rates of mixing given by the Ruelle spectrum of the hyperbolic map acting on this space, and solutions of the cohomological equation in primitive substitution subshifts for Hölder functions. The overarching theme is that considerations of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000415_inline1.png\"/> <jats:tex-math> $alpha $ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-Hölder regularity on Cantor sets go a long way.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224263","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}

{"title":"Symbolic dynamics for pointwise hyperbolic systems on open regions","authors":"CHUPENG WU, YUNHUA ZHOU","doi":"10.1017/etds.2024.47","DOIUrl":"https://doi.org/10.1017/etds.2024.47","url":null,"abstract":"Under certain conditions, we construct a countable Markov partition for pointwise hyperbolic diffeomorphism <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000476_inline1.png\"/> <jats:tex-math> $f:Mrightarrow M$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> on an open invariant subset <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000476_inline2.png\"/> <jats:tex-math> $Osubset M$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, which allows the Lyapunov exponents to be zero. From this partition, we define a symbolic extension that is finite-to-one and onto a subset of <jats:italic>O</jats:italic> that carries the same finite <jats:italic>f</jats:italic>-invariant measures as <jats:italic>O</jats:italic>. Our method relies upon shadowing theory of a recurrent-pointwise-pseudo-orbit that we introduce. As a canonical application, we estimate the number of closed orbits for <jats:italic>f</jats:italic>.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224267","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}

{"title":"Multiplication cubes and multiplication automata","authors":"JOHAN KOPRA","doi":"10.1017/etds.2024.44","DOIUrl":"https://doi.org/10.1017/etds.2024.44","url":null,"abstract":"We extend previously known two-dimensional multiplication tiling systems that simulate multiplication by two natural numbers <jats:italic>p</jats:italic> and <jats:italic>q</jats:italic> in base <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000440_inline1.png\"/> <jats:tex-math> $pq$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> to higher dimensional multiplication tessellation systems. We develop the theory of these systems and link different multiplication tessellation systems with each other via macrotile operations that glue cubes in one tessellation system into larger cubes of another tessellation system. The macrotile operations yield topological conjugacies and factor maps between cellular automata performing multiplication by positive numbers in various bases.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224265","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}

{"title":"Minimal and proximal examples of -stable and -approachable shift spaces","authors":"MELIH EMIN CAN, JAKUB KONIECZNY, MICHAL KUPSA, DOMINIK KWIETNIAK","doi":"10.1017/etds.2024.43","DOIUrl":"https://doi.org/10.1017/etds.2024.43","url":null,"abstract":"We study shift spaces over a finite alphabet that can be approximated by mixing shifts of finite type in the sense of (pseudo)metrics connected to Ornstein’s &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000439_inline3.png\"/&gt; &lt;jats:tex-math&gt; $bar {d}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; metric (&lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000439_inline4.png\"/&gt; &lt;jats:tex-math&gt; $bar {d}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-approachable shift spaces). The class of &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000439_inline5.png\"/&gt; &lt;jats:tex-math&gt; $bar {d}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-approachable shifts can be considered as a topological analog of measure-theoretical Bernoulli systems. The notion of &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000439_inline6.png\"/&gt; &lt;jats:tex-math&gt; $bar {d}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-approachability, together with a closely connected notion of &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000439_inline7.png\"/&gt; &lt;jats:tex-math&gt; $bar {d}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-shadowing, was introduced by Konieczny, Kupsa, and Kwietniak [&lt;jats:italic&gt;Ergod. Th. &amp; Dynam. Sys.&lt;/jats:italic&gt;43(3) (2023), 943–970]. These notions were developed with the aim of significantly generalizing specification properties. Indeed, many popular variants of the specification property, including the classic one and the almost/weak specification property, ensure &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000439_inline8.png\"/&gt; &lt;jats:tex-math&gt; $bar {d}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-approachability and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000439_inline9.png\"/&gt; &lt;jats:tex-math&gt; $bar {d}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-shadowing. Here, we study further properties and connections between &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000439_inline10.png\"/&gt; &lt;jats:tex-math&gt; $bar {d}$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-shadowing and &lt;jats:inline-formula&gt; &lt;jats:alternatives&gt; &lt;jats:inline-graphic xmlns:xlink=\"h","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224264","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}

{"title":"Equilibrium measures for two-sided shift spaces via dimension theory","authors":"VAUGHN CLIMENHAGA, JASON DAY","doi":"10.1017/etds.2024.46","DOIUrl":"https://doi.org/10.1017/etds.2024.46","url":null,"abstract":"Given a two-sided shift space on a finite alphabet and a continuous potential function, we give conditions under which an equilibrium measure can be described using a construction analogous to Hausdorff measure that goes back to the work of Bowen. This construction was previously applied to smooth uniformly and partially hyperbolic systems by the first author, Pesin, and Zelerowicz. Our results here apply to all subshifts of finite type and Hölder continuous potentials, but extend beyond this setting, and we also apply them to shift spaces with synchronizing words.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142185312","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}

{"title":"Non-rigidity of partially hyperbolic abelian -actions on tori","authors":"FEDERICO RODRIGUEZ HERTZ, ZHIREN WANG","doi":"10.1017/etds.2024.18","DOIUrl":"https://doi.org/10.1017/etds.2024.18","url":null,"abstract":"We prove that every genuinely partially hyperbolic <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S014338572400018X_inline2.png\"/> <jats:tex-math> $mathbb {Z}^r$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-action by toral automorphisms can be perturbed in <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S014338572400018X_inline3.png\"/> <jats:tex-math> $C^1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-topology, so that the resulting action is continuously conjugate, but not <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S014338572400018X_inline4.png\"/> <jats:tex-math> $C^1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-conjugate, to the original one.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-09-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142224272","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}