MIXING INVARIANT EXTREMAL DISTRIBUTIONAL CHAOS

被引：1

作者：

Wang, Lidong ^{[1
,2
]}

Wang, Xiang ^{[1
,2
]}

Lei, Fengchun ^{[1
]}

Liu, Heng ^{[2
]}

机构：

[1] Dalian Univ Technol, Sch Math Sci, Dalian 116024, Peoples R China

[2] Dalian Nationalities Univ, Sch Sci, Dalian 116600, Peoples R China

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2016年 / 36卷 / 11期

关键词：

Distributional chaos; scrambled set; SCRAMBLED SETS;

D O I：

10.3934/dcds.2016082

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper we give a complicated distributional chaos, that is, a mixing dynamical system with an invariant, extremal and transitive distributionally scrambled set.

引用

页码：6533 / 6538

页数：6

共 12 条

[1] THERE ARE NO CHAOTIC MAPPINGS WITH RESIDUAL SCRAMBLED SETS [J].

GEDEON, T .

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1987, 36 (03) :411-416

[2]

Huang W, 2001, ERGOD THEOR DYN SYST, V21, P77

[3] PERIOD 3 IMPLIES CHAOS [J].

LI, TY ;

YORKE, JA .

AMERICAN MATHEMATICAL MONTHLY, 1975, 82 (10) :985-992

[4] A chaotic function with a distributively scrambled set of full Lebesgue measure [J].

Liao, Gongfu ;

Wang, Lidong ;

Duan, Xiaodong .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 66 (10) :2274-2280

[5]

Misiurewicz M., 1985, ITERATION THEORY ITS

[6] DISTRIBUTIONAL CHAOS REVISITED [J].

Oprocha, Piotr .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2009, 361 (09) :4901-4925

[7] Invariant scrambled sets and distributional chaos [J].

Oprocha, Piotr .

DYNAMICAL SYSTEMS-AN INTERNATIONAL JOURNAL, 2009, 24 (01) :31-43

[8] MEASURES OF CHAOS AND A SPECTRAL DECOMPOSITION OF DYNAMICAL-SYSTEMS ON THE INTERVAL [J].

SCHWEIZER, B ;

SMITAL, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1994, 344 (02) :737-754

[9] Dense invariant open distributionally scrambled sets and closed distributionally scrambled sets [J].

Wang, Hui ;

Lei, Fengchun ;

Wang, Lidong .

TOPOLOGY AND ITS APPLICATIONS, 2014, 165 :110-120

[10] A note on the map with the whole space being a scrambled set [J].

Wang, Hui ;

Liao, Gongfu ;

Fan, Qinjie .

NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2009, 70 (06) :2400-2402

← 1 2 →