Topological sequence entropy for maps of the interval

被引：7

作者：

Hric, R ^{[1
]}

机构：

[1] Matej Bel Univ, Fac Nat Sci, Dept Math, SK-97401 Banska Bystrica, Slovakia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 1999年 / 127卷 / 07期

关键词：

adding machine; blowing up orbits; chaotic map; topological sequence entropy;

D O I：

10.1090/S0002-9939-99-04799-1

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A result by Franzova a and Smital shows that a continuous map of the interval into itself is chaotic if and only if its topological sequence entropy relative to a suitable increasing sequence of nonnegative integers is positive. In the present paper we prove that for any increasing sequence of nonnegative integers there exists a chaotic continuous map with zero topological sequence entropy relative to this sequence.

引用

页码：2045 / 2052

页数：8

共 10 条

[1] A CHARACTERIZATION OF OMEGA-LIMIT SETS OF MAPS OF THE INTERVAL WITH ZERO TOPOLOGICAL-ENTROPY [J].

BRUCKNER, AM ;

SMITAL, J .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1993, 13 :7-19

[2] CHARACTERIZATIONS OF WEAKLY CHAOTIC MAPS OF THE INTERVAL [J].

FEDORENKO, VV ;

SARKOVSKII, AN ;

SMITAL, J .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 110 (01) :141-148

[3] POSITIVE SEQUENCE TOPOLOGICAL-ENTROPY CHARACTERIZES CHAOTIC MAPS [J].

FRANZOVA, N ;

SMITAL, J .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1991, 112 (04) :1083-1086

[4]

GOODMAN TNT, 1974, P LOND MATH SOC, V29, P331

[5]

Gottschalk W, 1955, TOPOLOGICAL DYNAMICS

[6]

HARRISON J, 1981, LECT NOTES MATH, V898, P154

[7]

Kolyada S., 1996, Random and Computational Dynamics, V4, P205

[8] PERIOD 3 IMPLIES CHAOS [J].

LI, TY ;

YORKE, JA .

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

[9]

Misiurewicz M., 1979, LECT NOTES MATH, V729, P144

[10] CHAOTIC FUNCTIONS WITH ZERO TOPOLOGICAL-ENTROPY [J].

SMITAL, J .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 297 (01) :269-282

← 1 →