A note on transitivity in set-valued discrete systems

被引：91
|
作者：
Román-Flores, H [1 ]
机构：
[1] Univ Tarapaca, Dept Matemat, Arica, Chile
来源：
CHAOS SOLITONS & FRACTALS | 2003年 / 17卷 / 01期
关键词：
D O I：
10.1016/S0960-0779(02)00406-X
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
Let (X, d) be a metric space and f : X --> X is a continuous function. If we consider the space (K (X), H) of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d and (f) over bar : K(X) --> K(X), (f) over bar (A) = {f(a)/a is an element of A}, then the aim of this work is to show that (f) over bar transitive implies f transitive. Also, we give an example showing that f transitive does not implies (f) over bar transitive. (C) 2002 Elsevier Science Ltd. All rights reserved.
引用
收藏
页码：99 / 104
页数：6
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