Let X denote a compact metric space with distance d and F ： X×R→ X or Ft ： X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. T...Let X denote a compact metric space with distance d and F ： X×R→ X or Ft ： X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C0-flow. Moreover, we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points, and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.展开更多
Let M be a closed surface,orientable or non-orientable,and let f be a C0 flow on M of which all singular points are isolated.Then f has the pseudo-orbit tracing property if and only if (i) for any x∈M,both the ω-lim...Let M be a closed surface,orientable or non-orientable,and let f be a C0 flow on M of which all singular points are isolated.Then f has the pseudo-orbit tracing property if and only if (i) for any x∈M,both the ω-limit set ω(x) and the α-limit set α(x) of x contain only one orbit; (ii) for any regular point x of f,if ω(x) is not quasi-attracting,then α(x) is quasi-exclusive; (iii) every saddle point of f is strict,and at most 4-forked.展开更多
基金Supported by National Natural Science Foundations of China(Grant Nos.11261039,11661054)National Natural Science Foundation of Jiangxi(Grant No.20132BAB201009)
文摘Let X denote a compact metric space with distance d and F ： X×R→ X or Ft ： X→X denote a C0-flow. From the point of view of ergodic theory, all important dynamical behaviors take place on a full measure set. The aim of this paper is to introduce the notion of Banach upper density recurrent points and to show that the closure of the set of all Banach upper density recurrent points equals the measure center or the minimal center of attraction for a C0-flow. Moreover, we give an example to show that the set of quasi-weakly almost periodic points can be included properly in the set of Banach upper density recurrent points, and point out that the set of Banach upper density recurrent points can be included properly in the set of recurrent points.
基金Project supported by the National Natural Science Foundation of China.
文摘Let M be a closed surface,orientable or non-orientable,and let f be a C0 flow on M of which all singular points are isolated.Then f has the pseudo-orbit tracing property if and only if (i) for any x∈M,both the ω-limit set ω(x) and the α-limit set α(x) of x contain only one orbit; (ii) for any regular point x of f,if ω(x) is not quasi-attracting,then α(x) is quasi-exclusive; (iii) every saddle point of f is strict,and at most 4-forked.
