Devaney’s chaos on uniform limit maps |
| |
Authors: | Kesong Yan Fanping Zeng |
| |
Institution: | a Department of Mathematics, University of Science and Technology of China, Hefei, Anhui 230026, PR China b Department of Mathematics and Computer Science, Liuzhou Teachers College, Liuzhou, Guangxi 545004, PR China c Department of Mathematics, Shantou University, Shantou, Guangdong 515063, PR China |
| |
Abstract: | Let (X, d) be a compact metric space and fn : X → X a sequence of continuous maps such that (fn) 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 fn 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. |
| |
Keywords: | |
本文献已被 ScienceDirect 等数据库收录! |
|