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
In this note, we give the definition of the minimal centre of attraction for self-mapping on a compact metrizable space (for the case of flow, see Ref. [1]) and prove that the minimal centre of attraction coincides wi...In this note, we give the definition of the minimal centre of attraction for self-mapping on a compact metrizable space (for the case of flow, see Ref. [1]) and prove that the minimal centre of attraction coincides with the measure centre. Let (X, d) be a compact metrizable space and f: X→X be continuous.展开更多
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This work was supported by the National Basic Research Project "Nonlinear Science" and the National Natural Science Foundation of China
文摘In this note, we give the definition of the minimal centre of attraction for self-mapping on a compact metrizable space (for the case of flow, see Ref. [1]) and prove that the minimal centre of attraction coincides with the measure centre. Let (X, d) be a compact metrizable space and f: X→X be continuous.
