Let G be a graph and f: G → G be continuous. Denote by R(f) and Ω(f) the set of recurrent points and the set of non-wandering points of f respectively. Let Ω0 (f) = G and Ωn (f) =Ω(f|Ωn-1(f)) for all n ∈ N. The...Let G be a graph and f: G → G be continuous. Denote by R(f) and Ω(f) the set of recurrent points and the set of non-wandering points of f respectively. Let Ω0 (f) = G and Ωn (f) =Ω(f|Ωn-1(f)) for all n ∈ N. The minimal m ∈ NU {∞} such that Ωm(f) = Ωm+1(f) is called the depth of f. In this paper, we show that Ω2(f) = R(f) and the depth of f is at most 2. Furthermore, we obtain some properties of non-wandering points of f.展开更多
基金This work was supported by the Special Foundation of National Prior Basis Researches of China (Grant No.G1999075108)the National Natural Science Foundation of China (Grant No.10461001)the Natural Science Foundation of Guangxi (Grant Nos.0728002,0640205)
文摘Let G be a graph and f: G → G be continuous. Denote by R(f) and Ω(f) the set of recurrent points and the set of non-wandering points of f respectively. Let Ω0 (f) = G and Ωn (f) =Ω(f|Ωn-1(f)) for all n ∈ N. The minimal m ∈ NU {∞} such that Ωm(f) = Ωm+1(f) is called the depth of f. In this paper, we show that Ω2(f) = R(f) and the depth of f is at most 2. Furthermore, we obtain some properties of non-wandering points of f.
