逆极限空间上移位映射的性质

Properties of the Shift Maps on the Inverse Limit Space

研究了紧致度量空间上连续映射f:X→X的逆极限空间上移位映射σ:lim(X,f)→lim(X,f)的一些性质:移位映射σ的周期点集等于f的周期点集上的逆极限空间;X中有非回归点当且仅当道极限空间中有非回归点;逆极限空间的准周期点一定是周期点;f是拓扑传递的当且仅当σ_f是拓扑传递的.

The results about the shift map on the limit space of a compact metric space and a sole bonding map is proved: The periodic set of the shift map equals the inverse limit space of the periodic set of the sole bonding map; there is nonrecurrent point in X if there is nonrecurrent point in the inverse limit space; preperiodic point in the inverse limit space must be periodic point; the shift map on the inverse limit space is topologically transitive if its sole bonding map is topologically transitive.