In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model...In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model for the dynamics of gas absorption,展开更多
In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
In studying a dynamical system, one finds that there frequently exist some kinds of disturbance or false phenomenon. In order to remove them, we introduce a concept of the measure centre and in order to determine the ...In studying a dynamical system, one finds that there frequently exist some kinds of disturbance or false phenomenon. In order to remove them, we introduce a concept of the measure centre and in order to determine the structure of the measure centre, we also introduce another concept of the weakly almost periodic point. We totally determine the structure of the measure centre and exhibit an example to show that the measure centre may be contained properly in the motion centre and there is a system which is chaotic on the nonwandering set but has zero topological entropy.展开更多
Let X be a compact metric space, F : X ×R→ X be a continuous flow and x ∈ X a proper quasi-weakly almost periodic point, that is, x is quasi-weakly almost periodic but not weakly almost periodic. The aim of thi...Let X be a compact metric space, F : X ×R→ X be a continuous flow and x ∈ X a proper quasi-weakly almost periodic point, that is, x is quasi-weakly almost periodic but not weakly almost periodic. The aim of this paper is to investigate whether there exists an invariant measure generated by the orbit of x such that the support of this measure coincides with the minimal center of attraction of x? In order to solve the problem, two continuous flows are constructed. In one continuous flow,there exist a proper quasi-weakly almost periodic point and an invariant measure generated by its orbit such that the support of this measure coincides with its minimal center of attraction; and in the other,there is a proper quasi-weakly almost periodic point such that the support of any invariant measure generated by its orbit is properly contained in its minimal center of attraction. So the mentioned problem is sufficiently answered in the paper.展开更多
In this note, we introduce a new level on recurrent motion in discrete semi-dynamical systems, i.e. uniformly almost periodic (U.A.P.) points. For a U.A.P. point, we will prove that when the map is restricted on its c...In this note, we introduce a new level on recurrent motion in discrete semi-dynamical systems, i.e. uniformly almost periodic (U.A.P.) points. For a U.A.P. point, we will prove that when the map is restricted on its co-limit set, it is a homeomorphism, strictly ergodic and with zero-topological entropy. Moreover, we will give the co-limit set a description of a compact topological group structure.展开更多
Recently, He et al. [On quasi-weakly almost periodic points. Sci. China Math., 56, 597- 606 （2013）] constructed two binary sub-shifts to solve an open problem posed by Zhou and Feng in [Twelve open problems on the e...Recently, He et al. [On quasi-weakly almost periodic points. Sci. China Math., 56, 597- 606 （2013）] constructed two binary sub-shifts to solve an open problem posed by Zhou and Feng in [Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17, 493-502 （2004）]. In this paper, we study more dynamical properties of those two binary sub-shifts. We show that the first one has zero topological entropy and is transitive but not weakly mixing, while the second one has positive topological entropy and is strongly mixing.展开更多
In this paper, we consider stochastic Volterra-Levin equations. Based on semigroup of operators and fixed point method, under some suitable assumptions to ensure the existence and stability of pth-mean almost periodic...In this paper, we consider stochastic Volterra-Levin equations. Based on semigroup of operators and fixed point method, under some suitable assumptions to ensure the existence and stability of pth-mean almost periodic mild solutions to the system.展开更多
基金The NSF(001084)of Liaoning Provincethe Science Foundation of OUC and the NSF(10371010)of China
文摘In this paper, we investigate the pseudo almost periodicity of the unique bounded solution for a nonlinear hyperbolic equation with piecewise constant argument. The equation under consideration is a mathematical model for the dynamics of gas absorption,
基金supported by the National Natural Science Foundation of China（11371027） the Projects of Outstanding Young Talents of Universities in Anhui Province（gxyq2018116）+2 种基金 the Teaching Groups in Anhui Province（2016jxtd080,2015jxtd048） the NSF of Educational Bureau of Anhui Province（KJ2017A702,KJ2017A704） the NSF of Bozhou University（BZSZKYXM201302,BSKY201539）
文摘In this paper, the existence and uniqueness of almost periodic solutions for some infinite delay integral equations are discussed. By using Krasnoselskii fixed point theorem,some new results are obtained.
基金the National Education Foundation of Chinathe National Basic Research Project "Nonlinear Science".
文摘In studying a dynamical system, one finds that there frequently exist some kinds of disturbance or false phenomenon. In order to remove them, we introduce a concept of the measure centre and in order to determine the structure of the measure centre, we also introduce another concept of the weakly almost periodic point. We totally determine the structure of the measure centre and exhibit an example to show that the measure centre may be contained properly in the motion centre and there is a system which is chaotic on the nonwandering set but has zero topological entropy.
基金Supported by the National Natural Science Foundation of China(Grant No.11661054)
文摘Let X be a compact metric space, F : X ×R→ X be a continuous flow and x ∈ X a proper quasi-weakly almost periodic point, that is, x is quasi-weakly almost periodic but not weakly almost periodic. The aim of this paper is to investigate whether there exists an invariant measure generated by the orbit of x such that the support of this measure coincides with the minimal center of attraction of x? In order to solve the problem, two continuous flows are constructed. In one continuous flow,there exist a proper quasi-weakly almost periodic point and an invariant measure generated by its orbit such that the support of this measure coincides with its minimal center of attraction; and in the other,there is a proper quasi-weakly almost periodic point such that the support of any invariant measure generated by its orbit is properly contained in its minimal center of attraction. So the mentioned problem is sufficiently answered in the paper.
基金Project supported by the Foundation of Zhongshan University Advanced Research Centre.
文摘In this note, we introduce a new level on recurrent motion in discrete semi-dynamical systems, i.e. uniformly almost periodic (U.A.P.) points. For a U.A.P. point, we will prove that when the map is restricted on its co-limit set, it is a homeomorphism, strictly ergodic and with zero-topological entropy. Moreover, we will give the co-limit set a description of a compact topological group structure.
基金Supported by National Natural Science Foundation of China(Grant No.11261039)National Natural Science Foundation of Jiangxi Province(Grant No.20132BAB201009)the Innovation Fund Designated for Graduate Students of Jiangxi Province
文摘Recently, He et al. [On quasi-weakly almost periodic points. Sci. China Math., 56, 597- 606 （2013）] constructed two binary sub-shifts to solve an open problem posed by Zhou and Feng in [Twelve open problems on the exact value of the Hausdorff measure and on topological entropy： A brief survey of recent results. Nonlinearity, 17, 493-502 （2004）]. In this paper, we study more dynamical properties of those two binary sub-shifts. We show that the first one has zero topological entropy and is transitive but not weakly mixing, while the second one has positive topological entropy and is strongly mixing.
基金partially supported by the NNSF of China(Grant No.11271093)
文摘In this paper, we consider stochastic Volterra-Levin equations. Based on semigroup of operators and fixed point method, under some suitable assumptions to ensure the existence and stability of pth-mean almost periodic mild solutions to the system.
