摘要
研究了紧致度量空间X上连续映射f :X→X及其逆极限空间lim← (X ,f)上移位映射σf:lim← (X ,f) →lim← (X ,f)之间的相互关系 :f有不变集当且仅当σf 有不变集 ;f有稠密轨道当且仅当σf 有稠密轨道 ;X中有非回归点当且仅当lim← (X ,f)中有非回归点 ;f在X上是拓扑传递的当且仅当σf 在lim← (X ,f)是拓扑传递的 .
Study the relation of continuous mapping f:X→X on compact metric space X and the shift map σ f: lim ←(X,f)→ lim ←(X,f) on its inverse limit space lim ←(X,f): There is invariant set in X if and only if there is invariant set in lim ←(X,f); There is dense orbit in X if and only if there is dense orbit in lim ←(X,f); There is nonrecurrent point in X if and only if there is nonrecurent point in lim ←(X,f); The mapping f is topologically transitive if and only if the shift map σ f is topologically transitive.
出处
《北方交通大学学报》
CSCD
北大核心
2001年第3期16-18,共3页
Journal of Northern Jiaotong University
