Ergodic Theory and Dynamical Systems最新文献

{"title":"Regularity and linear response formula of the SRB measures for solenoidal attractors","authors":"CARLOS BOCKER, RICARDO BORTOLOTTI, ARMANDO CASTRO","doi":"10.1017/etds.2023.121","DOIUrl":"https://doi.org/10.1017/etds.2023.121","url":null,"abstract":"We show that a class of higher-dimensional hyperbolic endomorphisms admit absolutely continuous invariant probabilities whose densities are regular and vary differentiably with respect to the dynamical system. The maps we consider are skew-products given by <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385723001219_inline1.png\" /> <jats:tex-math> $T(x,y) = (E (x), C(x,y))$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, where <jats:italic>E</jats:italic> is an expanding map of <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385723001219_inline2.png\" /> <jats:tex-math> $mathbb {T}^u$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> and <jats:italic>C</jats:italic> is a contracting map on each fiber. If <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385723001219_inline3.png\" /> <jats:tex-math> $inf |!det DT| inf | (D_yC)^{-1}| ^{-2s}&gt;1$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> for some <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385723001219_inline4.png\" /> <jats:tex-math> ${s&lt;r-(({u+d})/{2}+1)}$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385723001219_inline5.png\" /> <jats:tex-math> $r geq 2$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>, and <jats:italic>T</jats:italic> satisfies a transversality condition between overlaps of iterates of <jats:italic>T</jats:italic> (a condition which we prove to be <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385723001219_inline6.png\" /> <jats:tex-math> $C^r$ </jats:tex-math> </jats:alternatives> </jats:inline-formula>-generic under mild assumptions), then the SRB measure <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385723001219_inline7.png\" /> <jats:tex-math> $mu _T$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> of <jats:italic>T</jats:italic> is absolutely continuous and its density <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S0143385723001219_inline8.png\" /> <jats:tex-math> $h_T$ </jats:tex-math> </jats:alternatives> </jats:inline-formula> belongs to the Sobolev space <jats:inline-formula> <jats:alternatives> <jats:inline-graphic xmlns:xlink=\"http://www.w3.org/1999/xlink\" mime-subtype=\"png\" xlink:href=\"S01433857230","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139771801","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":"ETS volume 44 issue 3 Cover and Front matter","authors":"","doi":"10.1017/etds.2023.81","DOIUrl":"https://doi.org/10.1017/etds.2023.81","url":null,"abstract":"","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139805805","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":"Lifting generic points","authors":"TOMASZ DOWNAROWICZ, BENJAMIN WEISS","doi":"10.1017/etds.2023.119","DOIUrl":"https://doi.org/10.1017/etds.2023.119","url":null,"abstract":"<p>Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190:S0143385723001190_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$(X,T)$</span></span></img></span></span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190:S0143385723001190_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$(Y,S)$</span></span></img></span></span> be two topological dynamical systems, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190:S0143385723001190_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$(X,T)$</span></span></img></span></span> has the weak specification property. Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190:S0143385723001190_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$xi $</span></span></img></span></span> be an invariant measure on the product system <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190:S0143385723001190_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$(Xtimes Y, Ttimes S)$</span></span></img></span></span> with marginals <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190:S0143385723001190_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$mu $</span></span></img></span></span> on <span>X</span> and <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190:S0143385723001190_inline7.png\"><span data-mathjax-type=\"texmath\"><span>$nu $</span></span></img></span></span> on <span>Y</span>, with <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190:S0143385723001190_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$mu $</span></span></img></span></span> ergodic. Let <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190:S0143385723001190_inline9.png\"><span data-mathjax-type=\"texmath\"><span>$yin Y$</span></span></img></span></span> be quasi-generic for <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203091301543-0170:S0143385723001190","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139688522","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":"Actions of discrete amenable groups into the normalizers of full groups of ergodic transformations","authors":"TOSHIHIKO MASUDA","doi":"10.1017/etds.2023.122","DOIUrl":"https://doi.org/10.1017/etds.2023.122","url":null,"abstract":"<p>We apply the Evans–Kishimoto intertwining argument to the classification of actions of discrete amenable groups into the normalizer of a full group of an ergodic transformation. Our proof does not depend on the types of ergodic transformations.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139688689","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":"ETS volume 44 issue 3 Cover and Back matter","authors":"","doi":"10.1017/etds.2023.82","DOIUrl":"https://doi.org/10.1017/etds.2023.82","url":null,"abstract":"","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139803420","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":"Multiplicity of topological systems","authors":"DAVID BURGUET, RUXI SHI","doi":"10.1017/etds.2023.118","DOIUrl":"https://doi.org/10.1017/etds.2023.118","url":null,"abstract":"<p>We define the topological multiplicity of an invertible topological system <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203084901549-0722:S0143385723001189:S0143385723001189_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$(X,T)$</span></span></img></span></span> as the minimal number <span>k</span> of real continuous functions <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203084901549-0722:S0143385723001189:S0143385723001189_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$f_1,ldots , f_k$</span></span></img></span></span> such that the functions <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203084901549-0722:S0143385723001189:S0143385723001189_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$f_icirc T^n$</span></span></img></span></span>, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203084901549-0722:S0143385723001189:S0143385723001189_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$nin {mathbb {Z}}$</span></span></img></span></span>, <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240203084901549-0722:S0143385723001189:S0143385723001189_inline5.png\"><span data-mathjax-type=\"texmath\"><span>$1leq ileq k,$</span></span></img></span></span> span a dense linear vector space in the space of real continuous functions on <span>X</span> endowed with the supremum norm. We study some properties of topological systems with finite multiplicity. After giving some examples, we investigate the multiplicity of subshifts with linear growth complexity.</p>","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139688710","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":"ETS volume 44 issue 3 Cover and Back matter","authors":"","doi":"10.1017/etds.2023.82","DOIUrl":"https://doi.org/10.1017/etds.2023.82","url":null,"abstract":"","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139863085","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":"ETS volume 44 issue 3 Cover and Front matter","authors":"","doi":"10.1017/etds.2023.81","DOIUrl":"https://doi.org/10.1017/etds.2023.81","url":null,"abstract":"","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139865420","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":"Eliminating Thurston obstructions and controlling dynamics on curves","authors":"MARIO BONK, MIKHAIL HLUSHCHANKA, ANNINA ISELI","doi":"10.1017/etds.2023.114","DOIUrl":"https://doi.org/10.1017/etds.2023.114","url":null,"abstract":"<p>Every Thurston map <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116121843232-0091:S0143385723001141:S0143385723001141_inline1.png\"><span data-mathjax-type=\"texmath\"><span>$fcolon S^2rightarrow S^2$</span></span></img></span></span> on a <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116121843232-0091:S0143385723001141:S0143385723001141_inline2.png\"><span data-mathjax-type=\"texmath\"><span>$2$</span></span></img></span></span>-sphere <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116121843232-0091:S0143385723001141:S0143385723001141_inline3.png\"><span data-mathjax-type=\"texmath\"><span>$S^2$</span></span></img></span></span> induces a pull-back operation on Jordan curves <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116121843232-0091:S0143385723001141:S0143385723001141_inline4.png\"><span data-mathjax-type=\"texmath\"><span>$alpha subset S^2smallsetminus {P_f}$</span></span></img></span></span>, where <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116121843232-0091:S0143385723001141:S0143385723001141_inline5.png\"><span data-mathjax-type=\"texmath\"><span>${P_f}$</span></span></img></span></span> is the postcritical set of <span>f</span>. Here the isotopy class <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116121843232-0091:S0143385723001141:S0143385723001141_inline6.png\"><span data-mathjax-type=\"texmath\"><span>$[f^{-1}(alpha )]$</span></span></img></span></span> (relative to <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116121843232-0091:S0143385723001141:S0143385723001141_inline7.png\"><span data-mathjax-type=\"texmath\"><span>${P_f}$</span></span></img></span></span>) only depends on the isotopy class <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240116121843232-0091:S0143385723001141:S0143385723001141_inline8.png\"><span data-mathjax-type=\"texmath\"><span>$[alpha ]$</span></span></img></span></span>. We study this operation for Thurston maps with four postcritical points. In this case, a Thurston obstruction for the map <span>f</span> can be seen as a fixed point of the pull-back operation. We show that if a Thurston map <span>f</span> with a hyperbolic orbifold and four postcritical points has a Thurston obstruction, then one can ‘blow up’ suitable arcs in the underlying <span><span><img data-mimesubtype=\"png\" data-type=\"\" src=\"https:/","PeriodicalId":50504,"journal":{"name":"Ergodic Theory and Dynamical Systems","volume":null,"pages":null},"PeriodicalIF":0.9,"publicationDate":"2024-01-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139481359","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":"ETS volume 44 issue 2 Cover and Back matter","authors":"","doi":"10.1017/etds.2023.80","DOIUrl":"https://doi.org/10.1017/etds.2023.80","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":"139380041","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}