Pub Date : 2021-09-12DOI: 10.1080/14689367.2021.1971623
T. N. H. Vu, Thieu Huy Nguyen, Anh Minh Le
We study the existence of admissible inertial manifolds for parabolic neutral functional differential equations of the form where the linear differential operator A is positive definite and self-adjoint with a discrete spectrum, the difference operator F is a bounded linear operator, and the delay nonlinear operator f is φ-Lipschitz for φ belonging to an admissible function space defined on . Our method is based on Lyapunov–Perron's equations, duality estimates in admissible spaces and F-induced trajectories. An application to heat transfer with delays in materials with memory is also given to illustrate our results.
{"title":"Admissible inertial manifolds for neutral equations and applications","authors":"T. N. H. Vu, Thieu Huy Nguyen, Anh Minh Le","doi":"10.1080/14689367.2021.1971623","DOIUrl":"https://doi.org/10.1080/14689367.2021.1971623","url":null,"abstract":"We study the existence of admissible inertial manifolds for parabolic neutral functional differential equations of the form where the linear differential operator A is positive definite and self-adjoint with a discrete spectrum, the difference operator F is a bounded linear operator, and the delay nonlinear operator f is φ-Lipschitz for φ belonging to an admissible function space defined on . Our method is based on Lyapunov–Perron's equations, duality estimates in admissible spaces and F-induced trajectories. An application to heat transfer with delays in materials with memory is also given to illustrate our results.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"608 - 630"},"PeriodicalIF":0.5,"publicationDate":"2021-09-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43154199","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 : 2021-07-21DOI: 10.1080/14689367.2023.2225463
O. Podvigina
Heteroclinic networks and cycles are invariant sets comprised of interacting nodes connected by heteroclinic trajectories. Often the sets are not asymptotically stable but attract a positive measure set from its small neighbourhood. This property is called fragmentary asymptotic stability (f.a.s.). The definition implies that if a stable cycle is a subset of a heteroclinic network, then the entire network is stable. In general, the converse is wrong. In the examples given in the literature, the presence of spiralling due to complex eigenvalues in the linearization around an equilibrium implies switching between subcycles of the f.a.s. network, thus preventing individual cycles from being stable. We study the behaviour of trajectories near a heteroclinic network comprised of two cycles where the eigenvalues of the linearizations are real. The trajectories can be attracted to one of the cycles, or they can switch regularly or irregularly between them. To describe regular switching, we introduce the notions of an omnicycle and its trail-stability, and prove conditions for trail-stability of an omnicycle in the considered network.
{"title":"Behaviour of trajectories near a two-cycle heteroclinic network","authors":"O. Podvigina","doi":"10.1080/14689367.2023.2225463","DOIUrl":"https://doi.org/10.1080/14689367.2023.2225463","url":null,"abstract":"Heteroclinic networks and cycles are invariant sets comprised of interacting nodes connected by heteroclinic trajectories. Often the sets are not asymptotically stable but attract a positive measure set from its small neighbourhood. This property is called fragmentary asymptotic stability (f.a.s.). The definition implies that if a stable cycle is a subset of a heteroclinic network, then the entire network is stable. In general, the converse is wrong. In the examples given in the literature, the presence of spiralling due to complex eigenvalues in the linearization around an equilibrium implies switching between subcycles of the f.a.s. network, thus preventing individual cycles from being stable. We study the behaviour of trajectories near a heteroclinic network comprised of two cycles where the eigenvalues of the linearizations are real. The trajectories can be attracted to one of the cycles, or they can switch regularly or irregularly between them. To describe regular switching, we introduce the notions of an omnicycle and its trail-stability, and prove conditions for trail-stability of an omnicycle in the considered network.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"38 1","pages":"576 - 596"},"PeriodicalIF":0.5,"publicationDate":"2021-07-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47897319","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 : 2021-07-16DOI: 10.1080/14689367.2021.1949436
Chiyi Luo, Yun Zhao
Given a topological dynamical system (X,T), i.e., T is a continuous transformation on a compact metric space X), that admits mistakes and an invariant measure, this paper proves the Brin–Katok formula in this case. In particular, this paper finds that it suffices to study a mistake function which is linear in n and monotonic with respect to Δ. Consequently, this paper shows the Brin–Katok formula for the mean Bowen ball replacing the Bowen metrics with the mean Bowen metrics. The results presented in this paper may have some applications in the study of other properties of a dynamical system which admits small errors.
{"title":"The Brin–Katok formula for dynamical systems admitting mistakes","authors":"Chiyi Luo, Yun Zhao","doi":"10.1080/14689367.2021.1949436","DOIUrl":"https://doi.org/10.1080/14689367.2021.1949436","url":null,"abstract":"Given a topological dynamical system (X,T), i.e., T is a continuous transformation on a compact metric space X), that admits mistakes and an invariant measure, this paper proves the Brin–Katok formula in this case. In particular, this paper finds that it suffices to study a mistake function which is linear in n and monotonic with respect to Δ. Consequently, this paper shows the Brin–Katok formula for the mean Bowen ball replacing the Bowen metrics with the mean Bowen metrics. The results presented in this paper may have some applications in the study of other properties of a dynamical system which admits small errors.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"560 - 571"},"PeriodicalIF":0.5,"publicationDate":"2021-07-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1949436","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41487720","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 : 2021-06-22DOI: 10.1080/14689367.2022.2100244
Nikolai Edeko, Henrik Kreidler, R. Nagel
We provide a dynamical proof of the van der Corput inequality for sequences in Hilbert spaces that is based on the Furstenberg correspondence principle. This is done by reducing the inequality to the mean ergodic theorem for contractions on Hilbert spaces. The key difficulty therein is that the Furstenberg correspondence principle is, a priori, limited to scalar-valued sequences. We, therefore, discuss how interpreting the Furstenberg correspondence principle via the Gelfand–Naimark–Segal construction for -algebras allows to study not just scalar but general Hilbert space-valued sequences in terms of unitary operators. This yields a proof of the van der Corput inequality in the spirit of the Furstenberg correspondence principle and the flexibility of this method is discussed via new proofs for different variants of the inequality.
基于Furstenberg对应原理，我们给出了Hilbert空间中序列的van der Corput不等式的一个动力学证明。这是通过将不等式简化为希尔伯特空间上收缩的平均遍历定理来实现的。其中的关键困难在于，Furstenberg对应原理先验地局限于标量值序列。因此，我们讨论了如何通过代数的Gelfand–Naimark–Segal构造来解释Furstenberg对应原理，从而不仅可以用酉算子研究标量序列，还可以用酉算子研究一般希尔伯特空间值序列。这根据Furstenberg对应原理的精神给出了van der Corput不等式的一个证明，并通过对不等式的不同变体的新证明讨论了该方法的灵活性。
{"title":"A dynamical proof of the van der Corput inequality","authors":"Nikolai Edeko, Henrik Kreidler, R. Nagel","doi":"10.1080/14689367.2022.2100244","DOIUrl":"https://doi.org/10.1080/14689367.2022.2100244","url":null,"abstract":"We provide a dynamical proof of the van der Corput inequality for sequences in Hilbert spaces that is based on the Furstenberg correspondence principle. This is done by reducing the inequality to the mean ergodic theorem for contractions on Hilbert spaces. The key difficulty therein is that the Furstenberg correspondence principle is, a priori, limited to scalar-valued sequences. We, therefore, discuss how interpreting the Furstenberg correspondence principle via the Gelfand–Naimark–Segal construction for -algebras allows to study not just scalar but general Hilbert space-valued sequences in terms of unitary operators. This yields a proof of the van der Corput inequality in the spirit of the Furstenberg correspondence principle and the flexibility of this method is discussed via new proofs for different variants of the inequality.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"648 - 665"},"PeriodicalIF":0.5,"publicationDate":"2021-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44727752","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 : 2021-06-18DOI: 10.1080/14689367.2021.1940868
C. Tadmon, Séverin Foko, A. Rendall
In this work, we propose and investigate a delay cell population model of hepatitis B virus (HBV) infection. We suppose spatial diffusion of free HBV particles, and use a Beddington-DeAngelis incidence function to describe viral infection. The model takes into account the exposed hepatocytes and the usually neglected humoral immune response. Moreover, a time delay is introduced to account for the transformation processes necessary for actual HBV production. We naturally find two threshold parameters, namely the basic reproduction number and the humoral immune response reproduction number which completely determine the global stability of the spatially homogeneous equilibria of the model obtained. By constructing appropriate Lyapunov functionals and using LaSalle's invariance principle we show that, if the disease-free equilibrium is globally asymptotically stable. Furthermore, we prove that the endemic equilibrium without humoral immune response and the endemic equilibrium with humoral immune response are globally asymptotically stable if and respectively. Finally, in one dimensional space, we perform some numerical simulations to illustrate the theoretical results obtained.
{"title":"Global stability analysis of a delay cell-population model of hepatitis B infection with humoral immune response","authors":"C. Tadmon, Séverin Foko, A. Rendall","doi":"10.1080/14689367.2021.1940868","DOIUrl":"https://doi.org/10.1080/14689367.2021.1940868","url":null,"abstract":"In this work, we propose and investigate a delay cell population model of hepatitis B virus (HBV) infection. We suppose spatial diffusion of free HBV particles, and use a Beddington-DeAngelis incidence function to describe viral infection. The model takes into account the exposed hepatocytes and the usually neglected humoral immune response. Moreover, a time delay is introduced to account for the transformation processes necessary for actual HBV production. We naturally find two threshold parameters, namely the basic reproduction number and the humoral immune response reproduction number which completely determine the global stability of the spatially homogeneous equilibria of the model obtained. By constructing appropriate Lyapunov functionals and using LaSalle's invariance principle we show that, if the disease-free equilibrium is globally asymptotically stable. Furthermore, we prove that the endemic equilibrium without humoral immune response and the endemic equilibrium with humoral immune response are globally asymptotically stable if and respectively. Finally, in one dimensional space, we perform some numerical simulations to illustrate the theoretical results obtained.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"537 - 559"},"PeriodicalIF":0.5,"publicationDate":"2021-06-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1940868","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44753295","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 : 2021-06-17DOI: 10.1080/14689367.2022.2106823
Luguis de los Santos Baños, Felipe Garc'ia-Ramos
Diam-mean equicontinuity is a dynamical property that has been of use in the study of non-periodic order. Using some type of ‘local’ skew product between a shift and an odometer looking cellular automaton (CA), we will show that there exists an almost diam-mean equicontinuous CA that is not almost equicontinuous (and hence not almost locally periodic). Previously, we constructed a CA that is almost mean equicontinuous [L.D.I.S. Baños and F. García-Ramos, Mean equicontinuity and mean sensitivity on cellular automata, Ergodic Theory Dynam. Systems 41 (12) (2021), pp. 3704–3721] but not almost diam-mean equicontinuous [L.D.I.S. Baños and F. García-Ramos, Diameter mean equicontinuity and cellular automata, Proceedings of the 27th International Workshop on Cellular Automata and Discrete Complex Systems, arXiv:2106.09641, 2021].
直径平均等连续性是一种动力学性质，在非周期序的研究中有着广泛的应用。使用移位和看起来像里程计的元胞自动机（CA）之间的某种类型的“局部”斜积，我们将证明存在一个几乎直径平均等连续的CA，它不是几乎等连续的（因此也不是几乎局部周期的）。以前，我们构造了一个几乎平均等连续的CA[L.D.I.S.Baños和F.García-Ramos，细胞自动机上的平均等连续性和平均灵敏度，遍历理论动态系统41（12）（2021），pp.3704–3721]，但不是几乎直径平均等连续[L.D.is.Baños and F。García-Ramos，Diameter均值等连续性与细胞自动机，第27届细胞自动机与离散复杂系统国际研讨会论文集，arXiv:210609641021]。
{"title":"Local non-periodic order and diam-mean equicontinuity on cellular automata","authors":"Luguis de los Santos Baños, Felipe Garc'ia-Ramos","doi":"10.1080/14689367.2022.2106823","DOIUrl":"https://doi.org/10.1080/14689367.2022.2106823","url":null,"abstract":"Diam-mean equicontinuity is a dynamical property that has been of use in the study of non-periodic order. Using some type of ‘local’ skew product between a shift and an odometer looking cellular automaton (CA), we will show that there exists an almost diam-mean equicontinuous CA that is not almost equicontinuous (and hence not almost locally periodic). Previously, we constructed a CA that is almost mean equicontinuous [L.D.I.S. Baños and F. García-Ramos, Mean equicontinuity and mean sensitivity on cellular automata, Ergodic Theory Dynam. Systems 41 (12) (2021), pp. 3704–3721] but not almost diam-mean equicontinuous [L.D.I.S. Baños and F. García-Ramos, Diameter mean equicontinuity and cellular automata, Proceedings of the 27th International Workshop on Cellular Automata and Discrete Complex Systems, arXiv:2106.09641, 2021].","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"37 1","pages":"666 - 683"},"PeriodicalIF":0.5,"publicationDate":"2021-06-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48838242","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 : 2021-06-13DOI: 10.1080/14689367.2021.1931814
Ya Wang, Ze‐hua Zhou
Let G be a locally compact second countable Hausdorff space with a positive regular Borel measure and ω is a weight on G. In this article, we provide necessary and sufficient conditions for the hypercyclic weighted translations acting on the weighted space in two different cases. Also, some examples are given to illustrate that the results in the first case generalize the characterizations on hypercyclicity for unilateral weighted shifts studied by Salas [16], and the results in the second case generalize Chen and Chu's work in [8]. Furthermore, we give characterizations of hypercyclicity for adjoint operators of these weighted translations.
{"title":"Hypercyclicity of weighted translations on locally compact Hausdorff spaces","authors":"Ya Wang, Ze‐hua Zhou","doi":"10.1080/14689367.2021.1931814","DOIUrl":"https://doi.org/10.1080/14689367.2021.1931814","url":null,"abstract":"Let G be a locally compact second countable Hausdorff space with a positive regular Borel measure and ω is a weight on G. In this article, we provide necessary and sufficient conditions for the hypercyclic weighted translations acting on the weighted space in two different cases. Also, some examples are given to illustrate that the results in the first case generalize the characterizations on hypercyclicity for unilateral weighted shifts studied by Salas [16], and the results in the second case generalize Chen and Chu's work in [8]. Furthermore, we give characterizations of hypercyclicity for adjoint operators of these weighted translations.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"507 - 526"},"PeriodicalIF":0.5,"publicationDate":"2021-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1931814","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49217326","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 : 2021-06-06DOI: 10.1080/14689367.2021.1927988
Zeya Mi
In this paper, we study the physical measures for a class of partially hyperbolic flows with mostly contracting centre. Let X be a vector field on a compact Riemannian manifold M with partially hyperbolic splitting . We prove that if the centre direction exhibits the asmptotically sectionally contracting behaviour with respect to Gibbs u-states, then X admits finitely many physical measures, and their basins cover Lebesgue almost all points of the ambient manifold. Moreover, when the unstable manifolds are dense, we prove that X admits only one physical measure whose basin covers a full Lebesgue measure subset. By tracing the physical measures via typical hyperbolic periodic orbits, we study the statistical stability of this kind of partially hyperbolic flows.
{"title":"Physical measures for partially hyperbolic flows with mostly contracting centre","authors":"Zeya Mi","doi":"10.1080/14689367.2021.1927988","DOIUrl":"https://doi.org/10.1080/14689367.2021.1927988","url":null,"abstract":"In this paper, we study the physical measures for a class of partially hyperbolic flows with mostly contracting centre. Let X be a vector field on a compact Riemannian manifold M with partially hyperbolic splitting . We prove that if the centre direction exhibits the asmptotically sectionally contracting behaviour with respect to Gibbs u-states, then X admits finitely many physical measures, and their basins cover Lebesgue almost all points of the ambient manifold. Moreover, when the unstable manifolds are dense, we prove that X admits only one physical measure whose basin covers a full Lebesgue measure subset. By tracing the physical measures via typical hyperbolic periodic orbits, we study the statistical stability of this kind of partially hyperbolic flows.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"427 - 444"},"PeriodicalIF":0.5,"publicationDate":"2021-06-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1927988","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47528522","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: 10.1080/14689367.2021.1929081
Huoyun Wang, X. Liao
In this paper, we introduce a notion of topological pressure, which is different from the LMW's and ML's for an iterated function system. We find out the properties of the topological pressure, which are more similar to the properties of the classical topological pressure than LMW's and ML's. For an iterated function system, we obtain a partial variational principle on topological pressure, which improves the LMW's related result. Finally, we give a lower bound estimation of the topological pressure for a Ruelle-expanding iterated function system. In particular, we point out the exponential growth rate of fixed points is a lower bound of WLLZ's topological entropy for a Ruelle-expanding iterated function system.
{"title":"Topological pressure for an iterated function system","authors":"Huoyun Wang, X. Liao","doi":"10.1080/14689367.2021.1929081","DOIUrl":"https://doi.org/10.1080/14689367.2021.1929081","url":null,"abstract":"In this paper, we introduce a notion of topological pressure, which is different from the LMW's and ML's for an iterated function system. We find out the properties of the topological pressure, which are more similar to the properties of the classical topological pressure than LMW's and ML's. For an iterated function system, we obtain a partial variational principle on topological pressure, which improves the LMW's related result. Finally, we give a lower bound estimation of the topological pressure for a Ruelle-expanding iterated function system. In particular, we point out the exponential growth rate of fixed points is a lower bound of WLLZ's topological entropy for a Ruelle-expanding iterated function system.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"483 - 506"},"PeriodicalIF":0.5,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1929081","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43453209","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: 10.1080/14689367.2021.1926430
Y. Tang, Jiandong Yin
Let be a nonautonomous dynamical system and μ be a Borel measure on X with a full support. The purpose of this paper is to introduce the concepts of large deviations theorem and expansive measure for nonautonomous discrete systems and investigate the dynamics of nonautonomous dynamical systems with the large deviations theorem. Actually, it is proved that is ergodicaly sensitive if the pair satisfies the large deviations theorem and is topologically strongly ergodic; is topologically ergodic if the pair satisfies the large deviations theorem in a sequence of positive integers; μ is expansive if the pair satisfies the large deviations theorem and is topologically strongly ergodic and each measurable set with positive measure with respect to μ has a nonempty interior.
{"title":"The dynamics of nonautonomous dynamical systems with the large deviations theorem","authors":"Y. Tang, Jiandong Yin","doi":"10.1080/14689367.2021.1926430","DOIUrl":"https://doi.org/10.1080/14689367.2021.1926430","url":null,"abstract":"Let be a nonautonomous dynamical system and μ be a Borel measure on X with a full support. The purpose of this paper is to introduce the concepts of large deviations theorem and expansive measure for nonautonomous discrete systems and investigate the dynamics of nonautonomous dynamical systems with the large deviations theorem. Actually, it is proved that is ergodicaly sensitive if the pair satisfies the large deviations theorem and is topologically strongly ergodic; is topologically ergodic if the pair satisfies the large deviations theorem in a sequence of positive integers; μ is expansive if the pair satisfies the large deviations theorem and is topologically strongly ergodic and each measurable set with positive measure with respect to μ has a nonempty interior.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":"36 1","pages":"416 - 426"},"PeriodicalIF":0.5,"publicationDate":"2021-06-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/14689367.2021.1926430","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41874675","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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