1 A kind of non-chaotic dynamical systems on the symbolic space Let A<sub>0</sub>=A<sub>1</sub>=A<sub>2</sub>=…={0,1},and X=multiply from i=0 to ∞ A<sub>i</sub>. For e...1 A kind of non-chaotic dynamical systems on the symbolic space Let A<sub>0</sub>=A<sub>1</sub>=A<sub>2</sub>=…={0,1},and X=multiply from i=0 to ∞ A<sub>i</sub>. For every integer k≥2, define metrics d<sub>k</sub>and d<sub>k</sub>’ on X by d<sub>k</sub>（a,b）=max{k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>|: i=0, 1, 2,…}, d<sub>k</sub>’（a, b）=sum from i=0 to ∞ k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>| forany a=（a<sub>0</sub>, a<sub>0</sub>, a<sub>2</sub>,…） and any b=（b<sub>0</sub>, b<sub>1</sub>, b<sub>2</sub>,…）∈X. It is easy to see that all d<sub>k</sub> andd<sub>k</sub>’ induce the same topological structure. Thus we now may only consider d≡d<sub>2</sub>. Thespace （X, d） is usually called a symbolic space. For simplicity, write X for （X, d）. It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Project supported by the National Natural Science Foundation of China.
文摘1 A kind of non-chaotic dynamical systems on the symbolic space Let A<sub>0</sub>=A<sub>1</sub>=A<sub>2</sub>=…={0,1},and X=multiply from i=0 to ∞ A<sub>i</sub>. For every integer k≥2, define metrics d<sub>k</sub>and d<sub>k</sub>’ on X by d<sub>k</sub>（a,b）=max{k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>|: i=0, 1, 2,…}, d<sub>k</sub>’（a, b）=sum from i=0 to ∞ k<sup>-i</sup>·|a<sub>i</sub>-b<sub>i</sub>| forany a=（a<sub>0</sub>, a<sub>0</sub>, a<sub>2</sub>,…） and any b=（b<sub>0</sub>, b<sub>1</sub>, b<sub>2</sub>,…）∈X. It is easy to see that all d<sub>k</sub> andd<sub>k</sub>’ induce the same topological structure. Thus we now may only consider d≡d<sub>2</sub>. Thespace （X, d） is usually called a symbolic space. For simplicity, write X for （X, d）. It
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.
