关于动力体系的全体非游荡点的集合M_1的注记

Remarks on the Set M_1 of all Nonwandering Points of a Dynamical System

证明了相空间X中全体非游荡点的集合M1可表示为[∪x∈Xω(x)],如果后者吸引X中的每一点.于此,X为一度量空间,(X,R,f)为一动力体系,ω(x)={y∈X: tn→∞,f(x,tn)→y},而一集A吸引点x意为dist(f(x,t),A)→0,当t→∞.

It is proved that the set M_1 of all nonwandering points in the phase space X can be represented by [∪x∈Xω(x)] if the latter attracts each point of X.Here X is a metric space,(X,R,f) is a dynamical system,ω(x)={y∈X:t_n→∞,f(x,t_n)→y},[E] is the closure of E in X,and a set A attracts a point x means dist(f(x,t),A)→0 as t→∞.