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 50 条

[1] Topological sequence entropy of interval maps
Cánovas, JS
[J]. NONLINEARITY, 2004, 17 (01) : 49 - 56
[2] Topological sequence entropy and topological dynamics of interval maps
Canovas, Jose S.
[J]. DYNAMICS OF CONTINUOUS DISCRETE AND IMPULSIVE SYSTEMS-SERIES A-MATHEMATICAL ANALYSIS, 2007, 14 (01): : 47 - 54
[3] Topological sequence entropy of w-limit sets of interval maps
Cánovas, JS
[J]. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2001, 7 (04) : 781 - 786
[4] Topological entropy of transitive maps of the interval
Block, Louis
Keesling, James
[J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2015, 21 (06) : 535 - 544
[5] On topological entropy of commuting interval maps
Cánovas, JS
Linero, A
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2002, 51 (07) : 1159 - 1165
[6] Permutations and topological entropy for interval maps
Misiurewicz, M
[J]. NONLINEARITY, 2003, 16 (03) : 971 - 976
[7] An interval counterexample on topological sequence entropy
Cánovas, JS
[J]. ACTA MATHEMATICA HUNGARICA, 2000, 88 (1-2) : 123 - 131
[8] An Interval Counterexample on Topological Sequence Entropy
J. S. Cánovas
[J]. Acta Mathematica Hungarica, 2000, 88 : 123 - 131
[9] TOPOLOGICAL-ENTROPY AND CHAOS OF INTERVAL MAPS
DU, BS
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1987, 11 (01) : 105 - 114
[10] ON THE TOPOLOGICAL-ENTROPY OF TRANSITIVE MAPS OF THE INTERVAL
COVEN, EM
HIDALGO, MC
[J]. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, 1991, 44 (02) : 207 - 213

← 1 2 3 4 5 →