| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 1890394 | Chaos, Solitons & Fractals | 2009 | 8 Pages |
Abstract
Let (X, d) be a compact metric space and f:X → X be continuous. Let f¯ be the natural extension of f to the space of all non-empty compact subsets of X endowed with the Hausdorff metric induced by d. In this paper, some dynamical properties of f and f¯ are considered. It is shown that positive topological entropy, Li–Yorke chaos and distributional chaos of f imply those of f¯, respectively, but not conversely. The results give an answer to the question proposed by Román-Flores.
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Xianfeng Ma, Bingzhe Hou, Gongfu Liao,