In ref. [1] Smale pointed out that the existence of minimal sets is an important problem. The main problem is to determine what kind of spaces are minimal with respect to some flows on it. A comprehensive report of th...In ref. [1] Smale pointed out that the existence of minimal sets is an important problem. The main problem is to determine what kind of spaces are minimal with respect to some flows on it. A comprehensive report of this problem was given in ref. [2]. The distal flows were studied in refs. [3, 4]. Recently, Komuro proved that the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
In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined...In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined on a general compact metric space but not on a continuum such that it has zero topological entropy and is not topologically mixing.展开更多
基金Project supported by the National Natural Science Foundation of China
文摘In ref. [1] Smale pointed out that the existence of minimal sets is an important problem. The main problem is to determine what kind of spaces are minimal with respect to some flows on it. A comprehensive report of this problem was given in ref. [2]. The distal flows were studied in refs. [3, 4]. Recently, Komuro proved that the
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.
基金Supported by the Foundation of the Jiangxi Education Department（GJJ11295） Sup- ported by the Natural Science Foundation of Jiangxi Province（20114BAB201006）
文摘In 2007, T Arai and N Chinen proved that every P -chaotic map from a continuum into itself has positive topological entropy and is topologically mixing. In this work, we show that there exists a P -chaotic map defined on a general compact metric space but not on a continuum such that it has zero topological entropy and is not topologically mixing.
基金Supported by the Support Program for 1 0 0 Young and Middle-Aged Disciplinary Leaders inGuangxi Higher Education Institution and SF of Guangxi(GSY0 1 3 5 0 2 7)
