On mixing property in set-valued discrete systems

被引：21

作者：

Gu, RB ^{[1
]}

Guo, WJ ^{[1
]}

机构：

[1] Nanjing Univ Finance & Econ, Sch Finance, Nanjing 210046, Peoples R China

来源：

CHAOS SOLITONS & FRACTALS | 2006年 / 28卷 / 03期

基金：

中国国家自然科学基金;

关键词：

D O I：

10.1016/j.chaos.2005.04.004

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let (X, d) be a compact metric space and f : X -> X be a continuous map. Let (K(X),H) be the space of all nonempty compact subsets of X endowed with the Hausdorff metric induced by d and (f) over bar : K(X) -> K(X) be the map defined by f (A) : {f (a) : a E A}. In this paper we investigate the relationships between the mixing property of (K(X), (f) over bar) and the mixing property of (X,f). In addition, we discuss specification for the set-valued discrete dynamical system (K(X), (f) over bar). (c) 2005 Elsevier Ltd. All rights reserved.

引用

页码：747 / 754

页数：8

共 15 条

[1]

[Anonymous], 1986, TEOR FUNKTSII FUNKTS

[2] ON DEVANEY DEFINITION OF CHAOS [J].

BANKS, J ;

BROOKS, J ;

CAIRNS, G ;

DAVIS, G ;

STACEY, P .

AMERICAN MATHEMATICAL MONTHLY, 1992, 99 (04) :332-334

[3] PERIODIC POINTS AND MEASURES FOR AXIOM-A DIFFEOMORPHISMS [J].

BOWEN, R .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 154 (FEB) :377-&

[4]

Denker M., 1976, LECT NOTES MATH, V527

[5]

Devaney R, 1987, An introduction to chaotic dynamical systems, DOI 10.2307/3619398

[6] On chaotic set-valued discrete dynamical systems [J].

Fedeli, A .

CHAOS SOLITONS & FRACTALS, 2005, 23 (04) :1381-1384

[7] Devaney's chaos or 2-scattering implies Li-Yorke's chaos [J].

Huang, W ;

Ye, XD .

TOPOLOGY AND ITS APPLICATIONS, 2002, 117 (03) :259-272

[8] WEAK DISJOINTNESS OF TRANSFORMATION GROUPS [J].

PELEG, R .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1972, 33 (01) :165-&

[9] A note on transitivity in set-valued discrete systems [J].

Román-Flores, H .

CHAOS SOLITONS & FRACTALS, 2003, 17 (01) :99-104

[10]

Shao S., 2004, THESIS U SCI TECHNOL

← 1 2 →