Ergodic Theory and Dynamical Systems最新文献

{"title":"Entropy, virtual Abelianness and Shannon orbit equivalence","authors":"DAVID KERR, HANFENG LI","doi":"10.1017/etds.2024.26","DOIUrl":"https://doi.org/10.1017/etds.2024.26","url":null,"abstract":"<p>We prove that if two free probability-measure-preserving (p.m.p.) <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240329070043690-0459:S0143385724000269:S0143385724000269_inline1.png\"><span data-mathjax-type=\"texmath\"><span>${mathbb Z}$</span></span></img></span></span>-actions are Shannon orbit equivalent, then they have the same entropy. The argument also applies more generally to yield the same conclusion for free p.m.p. actions of finitely generated virtually Abelian groups. Together with the isomorphism theorems of Ornstein and Ornstein–Weiss and the entropy invariance results of Austin and Kerr–Li in the non-virtually-cyclic setting, this shows that two Bernoulli actions of any non-locally-finite countably infinite amenable group are Shannon orbit equivalent if and only if they are measure conjugate. We also show, at the opposite end of the stochastic spectrum, that every <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240329070043690-0459:S0143385724000269:S0143385724000269_inline2.png\"><span data-mathjax-type=\"texmath\"><span>${mathbb Z}$</span></span></img></span></span>-odometer is Shannon orbit equivalent to the universal <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240329070043690-0459:S0143385724000269:S0143385724000269_inline3.png\"><span data-mathjax-type=\"texmath\"><span>${mathbb Z}$</span></span></img></span></span>-odometer.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"53 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140589961","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":"Scale recurrence lemma and dimension formula for Cantor sets in the complex plane","authors":"CARLOS GUSTAVO T. DE A. MOREIRA, ALEX MAURICIO ZAMUDIO ESPINOSA","doi":"10.1017/etds.2024.15","DOIUrl":"https://doi.org/10.1017/etds.2024.15","url":null,"abstract":"We prove a multidimensional conformal version of the scale recurrence lemma of Moreira and Yoccoz [Stable intersections of regular Cantor sets with large Hausdorff dimensions. <jats:italic>Ann. of Math. (2)</jats:italic>154(1) (2001), 45–96] for Cantor sets in the complex plane. We then use this new recurrence lemma, together with Moreira’s ideas in [Geometric properties of images of Cartesian products of regular Cantor sets by differentiable real maps. <jats:italic>Math. Z.</jats:italic>303 (2023), 3], to prove that under the right hypothesis for the Cantor sets <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000154_inline1.png\" /> <jats:tex-math> $K_1,ldots ,K_n$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and the function <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000154_inline2.png\" /> <jats:tex-math> $h:mathbb {C}^{n}to mathbb {R}^{l}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, the following formula holds: <jats:disp-formula> <jats:alternatives> <jats:graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385724000154_eqnu1.png\" /> <jats:tex-math> $$ begin{align*}HD(h(K_1times K_2 times cdotstimes K_n))=min {l,HD(K_1)+cdots+HD(K_n)}.end{align*} $$ </jats:tex-math> </jats:alternatives> </jats:disp-formula>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"22 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140300750","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 pressures of Hölder potentials and the fitting of analytic functions through them","authors":"LIANGANG MA, MARK POLLICOTT","doi":"10.1017/etds.2024.9","DOIUrl":"https://doi.org/10.1017/etds.2024.9","url":null,"abstract":"<p>The first part of this work is devoted to the study of higher derivatives of pressure functions of Hölder potentials on shift spaces with finitely many symbols. By describing the derivatives of pressure functions via the central limit theorem for the associated random processes, we discover some rigid relationships between derivatives of various orders. The rigidity imposes obstructions on fitting candidate convex analytic functions by pressure functions of Hölder potentials globally, which answers a question of Kucherenko and Quas. In the second part of the work, we consider fitting candidate analytic germs by pressure functions of locally constant potentials. We prove that all 1-level candidate germs can be realised by pressures of some locally constant potentials, as long as the number of symbols in the symbolic set is large enough. There are also some results on fitting 2-level germs by pressures of locally constant potentials obtained in the work.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"53 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140151558","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":"Approximate homomorphisms and sofic approximations of orbit equivalence relations","authors":"BEN HAYES, SRIVATSAV KUNNAWALKAM ELAYAVALLI","doi":"10.1017/etds.2024.22","DOIUrl":"https://doi.org/10.1017/etds.2024.22","url":null,"abstract":"We show that for every countable group, any sequence of approximate homomorphisms with values in permutations can be realized as the restriction of a sofic approximation of an orbit equivalence relation. Moreover, this orbit equivalence relation is uniquely determined by the invariant random subgroup of the approximate homomorphisms. We record applications of this result to recover various known stability and conjugacy characterizations for almost homomorphisms of amenable groups.","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"59 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140151529","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":"Measure transfer and S-adic developments for subshifts","authors":"NICOLAS BÉDARIDE, ARNAUD HILION, MARTIN LUSTIG","doi":"10.1017/etds.2024.19","DOIUrl":"https://doi.org/10.1017/etds.2024.19","url":null,"abstract":"<p>Based on previous work of the authors, to any <span>S</span>-adic development of a subshift <span>X</span> a ‘directive sequence’ of commutative diagrams is associated, which consists at every level <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240309085744099-0060:S0143385724000191:S0143385724000191_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$n geq 0$</span></span></img></span></span> of the measure cone and the letter frequency cone of the level subshift <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240309085744099-0060:S0143385724000191:S0143385724000191_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$X_n$</span></span></img></span></span> associated canonically to the given <span>S</span>-adic development. The issuing rich picture enables one to deduce results about <span>X</span> with unexpected directness. For instance, we exhibit a large class of minimal subshifts with entropy zero that all have infinitely many ergodic probability measures. As a side result, we also exhibit, for any integer <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240309085744099-0060:S0143385724000191:S0143385724000191_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$d geq 2$</span></span></img></span></span>, an <span>S</span>-adic development of a minimal, aperiodic, uniquely ergodic subshift <span>X</span>, where all level alphabets <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240309085744099-0060:S0143385724000191:S0143385724000191_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathcal A_n$</span></span></img></span></span> have cardinality <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240309085744099-0060:S0143385724000191:S0143385724000191_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$d,$</span></span></img></span></span> while none of the <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240309085744099-0060:S0143385724000191:S0143385724000191_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$d-2$</span></span></img></span></span> bottom level morphisms is recognizable in its level subshift <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240309085744099-0060:S0143385724000191:S0143385724000191_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$X_n subseteq mathcal A_n^{mathbb {Z}}$</span></span></img></span></span>.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"40 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140099758","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":"Invariant measures for -free systems revisited","authors":"AURELIA DYMEK, JOANNA KUŁAGA-PRZYMUS, DANIEL SELL","doi":"10.1017/etds.2024.7","DOIUrl":"https://doi.org/10.1017/etds.2024.7","url":null,"abstract":"For &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=\"S0143385724000075_inline2.png\" /&gt; &lt;jats:tex-math&gt; $mathscr {B} subseteq mathbb {N} $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, the &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=\"S0143385724000075_inline3.png\" /&gt; &lt;jats:tex-math&gt; $ mathscr {B} $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-free subshift &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=\"S0143385724000075_inline4.png\" /&gt; &lt;jats:tex-math&gt; $ X_{eta } $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; is the orbit closure of the characteristic function of the set 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=\"S0143385724000075_inline5.png\" /&gt; &lt;jats:tex-math&gt; $ mathscr {B} $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-free integers. We show that many results about invariant measures and entropy, previously only known for the hereditary closure 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=\"S0143385724000075_inline6.png\" /&gt; &lt;jats:tex-math&gt; $ X_{eta } $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;, have their analogues for &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=\"S0143385724000075_inline7.png\" /&gt; &lt;jats:tex-math&gt; $ X_{eta } $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; as well. In particular, we settle in the affirmative a conjecture of Keller about a description of such measures [G. Keller. Generalized heredity in &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=\"S0143385724000075_inline8.png\" /&gt; &lt;jats:tex-math&gt; $mathcal B$ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;-free systems. &lt;jats:italic&gt;Stoch. Dyn.&lt;/jats:italic&gt;21(3) (2021), Paper No. 2140008]. A central assumption in our work is that &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=\"S0143385724000075_inline9.png\" /&gt; &lt;jats:tex-math&gt; $eta ^{*} $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt; (the Toeplitz sequence that generates the unique minimal component 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=\"S0143385724000075_inline10.png\" /&gt; &lt;jats:tex-math&gt; $ X_{eta } $ &lt;/jats:tex-math&gt; &lt;/jats:alternatives&gt; &lt;/jats:inline-formula&gt;) is regular. From this, we obtai","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"37 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140075464","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-integrability of the restricted three-body problem","authors":"KAZUYUKI YAGASAKI","doi":"10.1017/etds.2024.4","DOIUrl":"https://doi.org/10.1017/etds.2024.4","url":null,"abstract":"<p>The problem of non-integrability of the circular restricted three-body problem is very classical and important in the theory of dynamical systems. It was partially solved by Poincaré in the nineteenth century: he showed that there exists no real-analytic first integral which depends analytically on the mass ratio of the second body to the total and is functionally independent of the Hamiltonian. When the mass of the second body becomes zero, the restricted three-body problem reduces to the two-body Kepler problem. We prove the non-integrability of the restricted three-body problem both in the planar and spatial cases for any non-zero mass of the second body. Our basic tool of the proofs is a technique developed here for determining whether perturbations of integrable systems which may be non-Hamiltonian are not meromorphically integrable near resonant periodic orbits such that the first integrals and commutative vector fields also depend meromorphically on the perturbation parameter. The technique is based on generalized versions due to Ayoul and Zung of the Morales–Ramis and Morales–Ramis–Simó theories. We emphasize that our results are not just applications of the theories.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"36 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140044204","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":"Bohr chaoticity of principal algebraic actions and Riesz product measures","authors":"AI HUA FAN, KLAUS SCHMIDT, EVGENY VERBITSKIY","doi":"10.1017/etds.2024.13","DOIUrl":"https://doi.org/10.1017/etds.2024.13","url":null,"abstract":"<p>For a continuous <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305151712838-0085:S0143385724000130:S0143385724000130_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {N}^d$</span></span></img></span></span> or <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305151712838-0085:S0143385724000130:S0143385724000130_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {Z}^d$</span></span></img></span></span> action on a compact space, we introduce the notion of Bohr chaoticity, which is an invariant of topological conjugacy and which is proved stronger than having positive entropy. We prove that all principal algebraic <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305151712838-0085:S0143385724000130:S0143385724000130_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {Z}$</span></span></img></span></span> actions of positive entropy are Bohr chaotic. The same is proved for principal algebraic actions of <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240305151712838-0085:S0143385724000130:S0143385724000130_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$mathbb {Z}^d$</span></span></img></span></span> with positive entropy under the condition of existence of summable homoclinic points.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"10 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140044286","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":"Tracial weights on topological graph algebras","authors":"JOHANNES CHRISTENSEN","doi":"10.1017/etds.2024.20","DOIUrl":"https://doi.org/10.1017/etds.2024.20","url":null,"abstract":"<p>We describe two kinds of regular invariant measures on the boundary path space <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304092108222-0628:S0143385724000208:S0143385724000208_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$partial E$</span></span></img></span></span> of a second countable topological graph <span>E</span>, which allows us to describe all extremal tracial weights on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304092108222-0628:S0143385724000208:S0143385724000208_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$C^{*}(E)$</span></span></img></span></span> which are not gauge-invariant. Using this description, we prove that all tracial weights on the C<span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304092108222-0628:S0143385724000208:S0143385724000208_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$^{*}$</span></span></img></span></span>-algebra <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304092108222-0628:S0143385724000208:S0143385724000208_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$C^{*}(E)$</span></span></img></span></span> of a second countable topological graph <span>E</span> are gauge-invariant when <span>E</span> is free. This in particular implies that all tracial weights on <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304092108222-0628:S0143385724000208:S0143385724000208_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$C^{*}(E)$</span></span></img></span></span> are gauge-invariant when <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240304092108222-0628:S0143385724000208:S0143385724000208_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$C^{*}(E)$</span></span></img></span></span> is simple and separable.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"67 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034050","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":"Patterson–Sullivan theory for groups with a strongly contracting element","authors":"RÉMI COULON","doi":"10.1017/etds.2024.10","DOIUrl":"https://doi.org/10.1017/etds.2024.10","url":null,"abstract":"<p>Using Patterson–Sullivan measures, we investigate growth problems for groups acting on a metric space with a strongly contracting element.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":"590 1","pages":""},"PeriodicalIF":0.9,"publicationDate":"2024-03-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"140034053","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}