非混沌的树映射

NON-CHAOTIC TREE MAPS

设f是树T上的连续自映射,SAP(f),ω(f);Ω(f)分别是f的强几乎周期点集,ω-极限集,非游荡集.本文证明下面几条是等价的:(i)f是非混沌的;(ii)SAP(f)=ω(f);(iii)fΩ(f)是逐点等度连续的;(iv)f│ω(f)是逐点等度连续的;(v)f是一致非混沌的。

Let f be a continuous self-map of a tree T, and SAP(f), w(f),Ω(f) be the set of strongly almost periodic points of f, the set of w-limit points of /, the set of non-wandering points off/ respectively. In this paper, the authors prove that the following statements are equivalent: (i)f is non-chaotic; (ii)SAP(f) = w(f); (iii)f|Ω(f) is pointwise equicontinuous; (iv)f|w(f) is pointwise equicontinuous; (v)f is uniformly non-chaotic.