Pub Date : 2021-06-03DOI: 10.1080/14689367.2021.1928605
Kengo Matsumoto
A λ-graph bisystem consists of a pair of two labelled Bratteli diagrams, that presents a two-sided subshift . We will construct a compact totally disconnected metric space consisting of tilings of a two-dimensional half plane from a λ-graph bisystem. The tiling space has a certain AF-equivalence relation written with a natural shift homeomorphism coming from the shift homeomorphism on the subshift . The equivalence relation yields an AF-algebra with an automorphism induced by . We will study invariance of the étale equivalence relation , the groupoid and the groupoid -algebras , under topological conjugacy of the presenting two-sided subshifts.
{"title":"An étale equivalence relation on a tiling space arising from a two-sided subshift and associated C*-algebras","authors":"Kengo Matsumoto","doi":"10.1080/14689367.2021.1928605","DOIUrl":"https://doi.org/10.1080/14689367.2021.1928605","url":null,"abstract":"A λ-graph bisystem consists of a pair of two labelled Bratteli diagrams, that presents a two-sided subshift . We will construct a compact totally disconnected metric space consisting of tilings of a two-dimensional half plane from a λ-graph bisystem. The tiling space has a certain AF-equivalence relation written with a natural shift homeomorphism coming from the shift homeomorphism on the subshift . The equivalence relation yields an AF-algebra with an automorphism induced by . We will study invariance of the étale equivalence relation , the groupoid and the groupoid -algebras , under topological conjugacy of the presenting two-sided subshifts.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"445 - 482"},"PeriodicalIF":0.5,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1928605","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43125414","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-03DOI: 10.1080/14689367.2021.1923659
Ping Huang, Chenwei Wang, Ercai Chen
In this paper, we give the definition of unstable topological entropy in mean u-metrics (the mean metrics in the unstable manifold) for partially hyperbolic systems. By establishing Katok's entropy formula of unstable metric entropy in mean u-metrics, we prove that the new unstable topological entropy is equal to the unstable topological entropy defined in Bowen u-metrics (the Bowen metrics in the unstable manifold). Finally, we obtain the variational principle related to the unstable topological entropy defined in mean u-metrics and unstable metric entropy, which states that the unstable topological entropy defined in mean u-metrics is the supremum of the unstable metric entropy taken over all invariant measures.
{"title":"Unstable topological entropy in mean u-metrics for partially hyperbolic systems","authors":"Ping Huang, Chenwei Wang, Ercai Chen","doi":"10.1080/14689367.2021.1923659","DOIUrl":"https://doi.org/10.1080/14689367.2021.1923659","url":null,"abstract":"In this paper, we give the definition of unstable topological entropy in mean u-metrics (the mean metrics in the unstable manifold) for partially hyperbolic systems. By establishing Katok's entropy formula of unstable metric entropy in mean u-metrics, we prove that the new unstable topological entropy is equal to the unstable topological entropy defined in Bowen u-metrics (the Bowen metrics in the unstable manifold). Finally, we obtain the variational principle related to the unstable topological entropy defined in mean u-metrics and unstable metric entropy, which states that the unstable topological entropy defined in mean u-metrics is the supremum of the unstable metric entropy taken over all invariant measures.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"387 - 403"},"PeriodicalIF":0.5,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1923659","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49319217","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-06-03DOI: 10.1080/14689367.2021.1924622
Hongfei Cui
For a class of piecewise convex maps f on the interval , we show that f has a unique absolutely continuous invariant probability measure μ with exponential decay of correlations, and we also present the explicit upper bounds on the rate. Moreover, we show the exponential loss of memory for a sequential dynamical system consisting of piecewise convex maps.
{"title":"Decay of correlations and memory loss for Lasota–Yorke convex maps","authors":"Hongfei Cui","doi":"10.1080/14689367.2021.1924622","DOIUrl":"https://doi.org/10.1080/14689367.2021.1924622","url":null,"abstract":"For a class of piecewise convex maps f on the interval , we show that f has a unique absolutely continuous invariant probability measure μ with exponential decay of correlations, and we also present the explicit upper bounds on the rate. Moreover, we show the exponential loss of memory for a sequential dynamical system consisting of piecewise convex maps.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"404 - 415"},"PeriodicalIF":0.5,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1924622","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42588424","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-05-01DOI: 10.1080/14689367.2022.2070351
H.‐C. Huang, Truyen Nguyen, C. B. Pickett
BIOCHEMISTRY. For the article ‘‘Regulation of the antioxidant response element by protein kinase C-mediated phosphorylation of NF-E2-related factor 2,’’ by H.-C. Huang, Truyen Nguyen, and Cecil B. Pickett, which appeared in number 23, November 7, 2000, of Proc. Natl. Acad. Sci. USA (97, 12475–12480), the authors note the following corrections due to printer’s errors. (i) The experimental concentrations of several reagents were listed erroneously in a number of places in the text and figure legends. They should have read as follows: tBHQ (100 mM), bNF (50 mM), U0126 (10 mM), and Ro-32–0432 (2 mM). (ii) In the section on the in vitro phosphorylation of Nrf2 by PKC (Fig. 5 legend and the corresponding Materials and Methods), the following concentrations should have appeared: Nrf2 (2 mM), PKC (5 nM), ATP (200 mM), and [g-33P]ATP (2 mCi). (iii) In addition, the following were omitted from the list of references:
{"title":"Correction","authors":"H.‐C. Huang, Truyen Nguyen, C. B. Pickett","doi":"10.1080/14689367.2022.2070351","DOIUrl":"https://doi.org/10.1080/14689367.2022.2070351","url":null,"abstract":"BIOCHEMISTRY. For the article ‘‘Regulation of the antioxidant response element by protein kinase C-mediated phosphorylation of NF-E2-related factor 2,’’ by H.-C. Huang, Truyen Nguyen, and Cecil B. Pickett, which appeared in number 23, November 7, 2000, of Proc. Natl. Acad. Sci. USA (97, 12475–12480), the authors note the following corrections due to printer’s errors. (i) The experimental concentrations of several reagents were listed erroneously in a number of places in the text and figure legends. They should have read as follows: tBHQ (100 mM), bNF (50 mM), U0126 (10 mM), and Ro-32–0432 (2 mM). (ii) In the section on the in vitro phosphorylation of Nrf2 by PKC (Fig. 5 legend and the corresponding Materials and Methods), the following concentrations should have appeared: Nrf2 (2 mM), PKC (5 nM), ATP (200 mM), and [g-33P]ATP (2 mCi). (iii) In addition, the following were omitted from the list of references:","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"354 - 355"},"PeriodicalIF":0.5,"publicationDate":"2021-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42090799","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-25DOI: 10.1080/14689367.2021.1914553
Liu Yunzhe
We consider polygonal billiards and we show the uniqueness of coding of non-periodic billiard trajectories in polygons whose holes have non-zero minimal diameters, generalising a theorem of Galperi...
{"title":"Uniqueness of billiard coding in polygons","authors":"Liu Yunzhe","doi":"10.1080/14689367.2021.1914553","DOIUrl":"https://doi.org/10.1080/14689367.2021.1914553","url":null,"abstract":"We consider polygonal billiards and we show the uniqueness of coding of non-periodic billiard trajectories in polygons whose holes have non-zero minimal diameters, generalising a theorem of Galperi...","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"1 1","pages":"1-24"},"PeriodicalIF":0.5,"publicationDate":"2021-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1914553","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60089153","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-06DOI: 10.1080/14689367.2021.1970115
Kengo Matsumoto
The class of normal subshifts includes irreducible nontrivial topological Markov shifts, irreducible nontrivial sofic shifts, synchronized systems, Dyck shifts, β-shifts, substitution minimal shifts, and so on. We will characterize one-sided topological conjugacy classes of normal subshifts in terms of the associated -algebras and its gauge actions with potentials. In particular, the one-sided topological conjugacy class of irreducible nontrivial sofic shifts are characterized in terms of the simple purely infinite Cuntz-Krieger algebras associated with the matrices of its left Fischer cover graphs and gauge actions with potentials. This generalizes the author's previous result for irreducible nontrivial topological Markov shifts and Cuntz-Krieger algebras with gauge actions.
{"title":"One-sided topological conjugacy of normal subshifts and gauge actions on the associated C*-algebras","authors":"Kengo Matsumoto","doi":"10.1080/14689367.2021.1970115","DOIUrl":"https://doi.org/10.1080/14689367.2021.1970115","url":null,"abstract":"The class of normal subshifts includes irreducible nontrivial topological Markov shifts, irreducible nontrivial sofic shifts, synchronized systems, Dyck shifts, β-shifts, substitution minimal shifts, and so on. We will characterize one-sided topological conjugacy classes of normal subshifts in terms of the associated -algebras and its gauge actions with potentials. In particular, the one-sided topological conjugacy class of irreducible nontrivial sofic shifts are characterized in terms of the simple purely infinite Cuntz-Krieger algebras associated with the matrices of its left Fischer cover graphs and gauge actions with potentials. This generalizes the author's previous result for irreducible nontrivial topological Markov shifts and Cuntz-Krieger algebras with gauge actions.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"586 - 607"},"PeriodicalIF":0.5,"publicationDate":"2021-04-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48489522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-03DOI: 10.1080/14689367.2021.1905777
René Rühr
We provide a quantification of the uniqueness of Gibbs measure for topologically mixing countable Markov shifts with locally Hölder continuous potentials. Corollaries for speed of convergence for approximation by finite subsystems are also given.
{"title":"Pressure inequalities for Gibbs measures of countable Markov shifts","authors":"René Rühr","doi":"10.1080/14689367.2021.1905777","DOIUrl":"https://doi.org/10.1080/14689367.2021.1905777","url":null,"abstract":"We provide a quantification of the uniqueness of Gibbs measure for topologically mixing countable Markov shifts with locally Hölder continuous potentials. Corollaries for speed of convergence for approximation by finite subsystems are also given.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"332 - 339"},"PeriodicalIF":0.5,"publicationDate":"2021-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1905777","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43553942","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-04-02DOI: 10.1080/14689367.2021.1978394
Kiho Park, Tianyu Wang
In this paper, we study multifractal spectra of the geodesic flows on compact rank 1 surfaces without focal points. We compute the entropy of the level sets for the Lyapunov exponents and establish a lower bound for their Hausdorff dimension in terms of the pressure function and its Legendre transform. In doing so, we employ and generalize results of Burns and Gelfert for non-positively curved surfaces and construct an increasingly nested sequence of basic sets in the complement of the singular set on which the geodesic flow is non-uniformly hyperbolic. Such a sequence of basic sets eventually contains any given basic set.
{"title":"Multifractal analysis of geodesic flows on surfaces without focal points","authors":"Kiho Park, Tianyu Wang","doi":"10.1080/14689367.2021.1978394","DOIUrl":"https://doi.org/10.1080/14689367.2021.1978394","url":null,"abstract":"In this paper, we study multifractal spectra of the geodesic flows on compact rank 1 surfaces without focal points. We compute the entropy of the level sets for the Lyapunov exponents and establish a lower bound for their Hausdorff dimension in terms of the pressure function and its Legendre transform. In doing so, we employ and generalize results of Burns and Gelfert for non-positively curved surfaces and construct an increasingly nested sequence of basic sets in the complement of the singular set on which the geodesic flow is non-uniformly hyperbolic. Such a sequence of basic sets eventually contains any given basic set.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"656 - 684"},"PeriodicalIF":0.5,"publicationDate":"2021-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46604884","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-22DOI: 10.1080/14689367.2021.1893661
Waleed Aziz, A. Amen, C. Pantazi
We consider a three-dimensional vector field with quadratic nonlinearities and in general none of the axis plane is invariant. For our investigation, we are interesting in the case of – resonance at the origin. Hence, we deal with a nine parametric family of quadratic systems and our purpose is to understand the mechanisms of local integrability. By computing some obstructions, knowing as resonant focus quantities, first we present necessary conditions that guarantee the existence of two independent local first integrals at the origin. For this reason Gröbner basis and some other algorithms are employed. Then we examine the cases where the origin is linearizable. Some techniques like existence of invariant surfaces and Jacobi multipliers, Darboux method, properties of linearizable nodes of two dimensional systems and power series arguments are used to prove the sufficiency of the obtained conditions. For a particular three-parametric subfamily, we provide conditions on the parameters to guarantee the non-existence of a polynomial first integral.
{"title":"Integrability and linearizability of a family of three-dimensional quadratic systems","authors":"Waleed Aziz, A. Amen, C. Pantazi","doi":"10.1080/14689367.2021.1893661","DOIUrl":"https://doi.org/10.1080/14689367.2021.1893661","url":null,"abstract":"We consider a three-dimensional vector field with quadratic nonlinearities and in general none of the axis plane is invariant. For our investigation, we are interesting in the case of – resonance at the origin. Hence, we deal with a nine parametric family of quadratic systems and our purpose is to understand the mechanisms of local integrability. By computing some obstructions, knowing as resonant focus quantities, first we present necessary conditions that guarantee the existence of two independent local first integrals at the origin. For this reason Gröbner basis and some other algorithms are employed. Then we examine the cases where the origin is linearizable. Some techniques like existence of invariant surfaces and Jacobi multipliers, Darboux method, properties of linearizable nodes of two dimensional systems and power series arguments are used to prove the sufficiency of the obtained conditions. For a particular three-parametric subfamily, we provide conditions on the parameters to guarantee the non-existence of a polynomial first integral.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"317 - 331"},"PeriodicalIF":0.5,"publicationDate":"2021-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1893661","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47707772","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2021-03-20DOI: 10.1080/14689367.2022.2031890
Pablo G. Barrientos, Yushi Nakano, Artem Raibekas, M. Roldán
We systematically investigate examples of non-hyperbolic dynamical systems having irregular sets of full topological entropy and full Hausdorff dimension. The examples include some partially hyperbolic systems and geometric Lorenz flows. We also pose interesting questions for future research.
{"title":"Topological entropy and Hausdorff dimension of irregular sets for non-hyperbolic dynamical systems","authors":"Pablo G. Barrientos, Yushi Nakano, Artem Raibekas, M. Roldán","doi":"10.1080/14689367.2022.2031890","DOIUrl":"https://doi.org/10.1080/14689367.2022.2031890","url":null,"abstract":"We systematically investigate examples of non-hyperbolic dynamical systems having irregular sets of full topological entropy and full Hausdorff dimension. The examples include some partially hyperbolic systems and geometric Lorenz flows. We also pose interesting questions for future research.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"181 - 210"},"PeriodicalIF":0.5,"publicationDate":"2021-03-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47733858","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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