摘要
设X为紧致度量空间,f∶X→X是连续映射,称(X,f)为拓扑动力系统.为揭示系统(X,f)的动力学性质,利用逆极限的方法证明了系统的任开覆盖有有限复杂性当且仅当它的逆极限系统的任开覆盖有有限复杂性,系统是扩散的当且仅当逆极限系统是扩散的.
We obtained that: the system(X , ∫) is equicontinuous if the inverse limit system(lim(X , ∫) , σ∫) is equicontinuous; any finte cover by open sets of (X , ∫) has bounded complexity if any finte cover by open sets of (lim(X , ∫) , σ∫) has bounded complexity; the system (X , ∫) is scattering if the inverse limit system(lim(X , ∫), σ∫) is scattering.
出处
《湖南师范大学自然科学学报》
EI
CAS
北大核心
2004年第2期26-28,74,共4页
Journal of Natural Science of Hunan Normal University
