Devaney's chaos on uniform limit maps

作者：Yan, Kesong^*; Zeng, Fanping; Zhang, Gengrong

来源：Chaos Solitons & Fractals, 2011, 44(7): 522-525.

DOI：10.1016/j.chaos.2011.05.006

Let (X, d) be a compact metric space and f(n):X -> X a sequence of continuous maps such that (f(n)) converges uniformly to a map f. The purpose of this paper is to study the Devaney's chaos on the uniform limit f. On the one hand, we show that f is not necessarily transitive even if all f(n) mixing, and the sensitive dependence on initial conditions may not been inherited to f even if the iterates of the sequence have some uniform convergence, which correct two wrong claims in [1]. On the other hand, we give some equivalence conditions for the uniform limit f to be transitive and to have sensitive dependence on initial conditions. Moreover, we present an example to show that a non-transitive sequence may converge uniformly to a transitive map.

• 出版日期2011-7
• 单位汕头大学; 广西科技师范学院