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Dynamical Systems-An International Journal最新文献

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Hausdorff and packing dimensions of homogeneous product Moran sets 齐次积Moran集的Hausdorff和包装尺寸
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-05-10 DOI: 10.1080/14689367.2023.2208533
Qi Wang
{"title":"Hausdorff and packing dimensions of homogeneous product Moran sets","authors":"Qi Wang","doi":"10.1080/14689367.2023.2208533","DOIUrl":"https://doi.org/10.1080/14689367.2023.2208533","url":null,"abstract":"Let be the collection of homogeneous product Moran sets determined by two sequences of positive integers , and two sequences of positive numbers , . We obtain the maximal and minimal values of the Hausdorff and packing dimensions of elements in .","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-05-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45448043","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}
引用次数: 0
Dynamics of stochastic FitzHugh–Nagumo system on unbounded domains with memory 记忆无界域上随机FitzHugh–Nagumo系统的动力学
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-04-04 DOI: 10.1080/14689367.2023.2194522
Bui Kim My, N. Toan
{"title":"Dynamics of stochastic FitzHugh–Nagumo system on unbounded domains with memory","authors":"Bui Kim My, N. Toan","doi":"10.1080/14689367.2023.2194522","DOIUrl":"https://doi.org/10.1080/14689367.2023.2194522","url":null,"abstract":"In this paper, we consider the non-autonomous stochastic FitzHugh–Nagumo system with hereditary memory and a very large class of nonlinearities, which has no restriction on the upper growth of the nonlinearity. The existence of a random pullback attractor is established for this system in all N-dimensional space.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-04-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41564087","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}
引用次数: 0
Structure and dimension of invariant subsets of expanding Markov maps and joint invariance 展开马尔可夫映射不变子集的结构、维数及联合不变性
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-03-26 DOI: 10.1080/14689367.2023.2194520
Georgios Lamprinakis
{"title":"Structure and dimension of invariant subsets of expanding Markov maps and joint invariance","authors":"Georgios Lamprinakis","doi":"10.1080/14689367.2023.2194520","DOIUrl":"https://doi.org/10.1080/14689367.2023.2194520","url":null,"abstract":"A long-standing question is what invariant subsets can be shared by two maps acting on the same space. A similar question stands for invariant measures. A particular interesting case are expanding Markov maps of the circle. If the two involved maps are commuting the answer is almost complete. However very little is known in the non-commutative case. A first step is to analyse the structure of the invariant subsets of a single map. For a mapping of the circle of class , , we study the topological structure of the set consisting of all compact invariant subsets. Furthermore for a fixed such mapping we examine locally, in the category sense, how big is the set of all maps that have at least one non-trivial joint invariant compact subset. Lastly we show the strong dimensional relation between the maximal invariant subset of a given Markov map contained in a subinterval and the set of all right endpoints of its invariant subsets that are contained in the same subinterval, , as well as the continuous dependence of the dimension on the endpoints of the subinterval .","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41848452","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}
引用次数: 0
The 0:1 resonance bifurcation associated with the supercritical Hamiltonian pitchfork bifurcation 与超临界哈密顿干草叉分岔相关的0:1共振分岔
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-03-26 DOI: 10.1080/14689367.2023.2194521
Xing Zhou
{"title":"The 0:1 resonance bifurcation associated with the supercritical Hamiltonian pitchfork bifurcation","authors":"Xing Zhou","doi":"10.1080/14689367.2023.2194521","DOIUrl":"https://doi.org/10.1080/14689367.2023.2194521","url":null,"abstract":"We consider the non-semisimple 0:1 resonance (i.e. the unperturbed equilibrium has two purely imaginary eigenvalues ( and ) and a non-semisimple double-zero one) Hamiltonian bifurcation with one distinguished parameter, which corresponds to the supercritical Hamiltonian pitchfork bifurcation. Based on BCKV singularity theory established by [H.W. Broer, S. -N. Chow, Y. Kim, and G. Vegter, A normally elliptic Hamiltonian bifurcation, Z. Angew. Math. Phys. 44 (3) (1993), pp. 389–432], this bifurcation essentially triggered by the reversible universal unfolding with respect to BCKV-restricted morphisms of the planar non-semisimple singularity (the is regarded as distinguished parameter with respect to the external parameter λ). We first give the plane bifurcation diagram of the integrable Hamiltonian on each level of integral in detail, which is related to the usual supercritical Hamiltonian pitchfork bifurcation. Then, we use the -symmetry generated by the additional pair of imaginary eigenvalues to reconstruct the above plane bifurcation phenomenon caused by the zero eigenvalue pair into the case with two degrees of freedom. Finally, we prove the persistence of typical bifurcation scenarios (e.g. 2-dimensional invariant tori and the symmetric homoclinic orbit) under the small Hamiltonian perturbations, as proposed by [H.W. Broer, S. -N. Chow, Y. Kim, and G. Vegter, A normally elliptic Hamiltonian bifurcation, Z. Angew. Math. Phys. 44 (3) (1993), pp. 389–432]. An example system (the coupled Duffing oscillator) with strong linear coupling and weak local nonlinearity is given for this bifurcation.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43798492","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}
引用次数: 0
A generalization of van der Corput's difference theorem with applications to recurrence and multiple ergodic averages van der Corput差分定理的推广及其在递推和多重遍历平均中的应用
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-03-21 DOI: 10.1080/14689367.2023.2230160
S. Farhangi
{"title":"A generalization of van der Corput's difference theorem with applications to recurrence and multiple ergodic averages","authors":"S. Farhangi","doi":"10.1080/14689367.2023.2230160","DOIUrl":"https://doi.org/10.1080/14689367.2023.2230160","url":null,"abstract":"We prove a generalization of van der Corput's difference theorem for sequences of vectors in a Hilbert space. This generalization is obtained by establishing a connection between sequences of vectors in the first Hilbert space with a vector in a new Hilbert space whose spectral type with respect to a certain unitary operator is absolutely continuous with respect to the Lebesgue measure. We use this generalization to obtain applications regarding recurrence and multiple ergodic averages when we have measure preserving automorphisms T and S that do not necessarily commute, but T has a maximal spectral type that is mutually singular with the Lebesgue measure.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-03-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44136068","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}
引用次数: 1
Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps 展开马尔可夫映射的Lipschitz函数下循环和收缩目标集的Hausdorff维数
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-02-24 DOI: 10.1080/14689367.2023.2184328
Na Yuan, Bing Li
{"title":"Hausdorff dimensions of recurrent and shrinking target sets under Lipschitz functions for expanding Markov maps","authors":"Na Yuan, Bing Li","doi":"10.1080/14689367.2023.2184328","DOIUrl":"https://doi.org/10.1080/14689367.2023.2184328","url":null,"abstract":"Let T be an expanding Markov map with a repeller E defined on . This paper concerns the Hausdorff dimension of the sets and where is a sequence of Lipschitz functions with a uniform Lipschitz constant, , f is a positive continuous function on , is the sum and ψ is a positive function defined on . The results can be applied to cookie-cutter dynamical systems and continued fraction dynamical systems, etc.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-24","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42646541","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}
引用次数: 2
Upper semicontinuity of the global attractor for Bresse system with second sound 具有第二声的Bresse系统全局吸引子的上半连续性
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-02-23 DOI: 10.1080/14689367.2023.2182182
M. Freitas, A. Ramos, M. Aouadi, D. S. Almeida Júnior
{"title":"Upper semicontinuity of the global attractor for Bresse system with second sound","authors":"M. Freitas, A. Ramos, M. Aouadi, D. S. Almeida Júnior","doi":"10.1080/14689367.2023.2182182","DOIUrl":"https://doi.org/10.1080/14689367.2023.2182182","url":null,"abstract":"In this paper, we study the long-time dynamics of Bresse system under mixed homogeneous Dirichlet–Neumann boundary conditions. The heat conduction is given by Cattaneo's law. Only the shear angle displacement is damped via the dissipation from the Cattaneo's law, and the vertical displacement and the longitudinal displacement are free. Under quite general assumptions on the source term and based on the semigroup theory, we establish the global well-posedness and the existence of global attractors with finite fractal dimension in natural space energy. Finally, we prove the upper semicontinuous with respect to the relaxation time τ as it converges to zero.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43335676","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}
引用次数: 0
Topological pressure of a factor map for nonautonomous dynamical systems 非自治动力系统因子映射的拓扑压力
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-02-23 DOI: 10.1080/14689367.2023.2182183
Lei Liu, Cao Zhao
{"title":"Topological pressure of a factor map for nonautonomous dynamical systems","authors":"Lei Liu, Cao Zhao","doi":"10.1080/14689367.2023.2182183","DOIUrl":"https://doi.org/10.1080/14689367.2023.2182183","url":null,"abstract":"Let be a compact metric space and be a sequence of continuous maps from X to itself. Denote by the sequence and by the induced nonautonomous dynamical system. In this paper, we give the definitions of upper capacity topological pressure and Pesin-Pitskel topological pressure on a noncompact subset for nonautonomous dynamical systems from the dimension theory. Moreover, we propose the equivalent definition of Pesin-Pitskel topological pressure and investigate some properties of topological pressure. In contrast to Bowen's inequality, we discuss a relation for two topological pressures and establish an inequality formula for two topological pressures with a factor map of nonautonomous dynamical systems.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48472157","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}
引用次数: 0
Bratteli diagrams for bounded topological speedups 有界拓扑加速的Bratteli图
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-02-19 DOI: 10.1080/14689367.2023.2170775
Drew D. Ash, A. Dykstra, M. LeMasurier
{"title":"Bratteli diagrams for bounded topological speedups","authors":"Drew D. Ash, A. Dykstra, M. LeMasurier","doi":"10.1080/14689367.2023.2170775","DOIUrl":"https://doi.org/10.1080/14689367.2023.2170775","url":null,"abstract":"ABSTRACT A bounded topological speedup of a Cantor minimal system is a minimal system , where for some bounded function , or any system topologically conjugate to such an . Assuming the system is represented by a properly ordered Bratteli diagram , we provide a method for constructing a new, perfectly ordered Bratteli diagram that represents the sped-up system . The diagram relates back to in a manner that enables us to see how certain dynamical properties are preserved under speedup. As an application, in the case that is a substitution minimal system, we show how to use to write an explicit substitution rule that generates the sped-up system , answering an open question from [L. Alvin, D.D. Ash, and N.S. Ormes, Bounded topological speedups, Dyn. Syst. 33(2) (2018), pp. 303–331.].","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43041553","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}
引用次数: 0
On codimension one special Anosov endomorphisms 余维一特殊的Anosov自同态
IF 0.5 4区 数学
Dynamical Systems-An International Journal Pub Date : 2023-02-05 DOI: 10.1080/14689367.2022.2164708
Xiang Zhang
{"title":"On codimension one special Anosov endomorphisms","authors":"Xiang Zhang","doi":"10.1080/14689367.2022.2164708","DOIUrl":"https://doi.org/10.1080/14689367.2022.2164708","url":null,"abstract":"We show that if a closed smooth n-manifold M admits a u-dimension one special Anosov endomorphism f, then M is homeomorphic to and f is topologically conjugate to a hyperbolic toral endomorphism. Moreover, any u-dimension one special Anosov endomorphism is transitive and the stable foliation is minimal.","PeriodicalId":50564,"journal":{"name":"Dynamical Systems-An International Journal","volume":null,"pages":null},"PeriodicalIF":0.5,"publicationDate":"2023-02-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43265856","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}
引用次数: 0
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