ON THE TOPOLOGICAL-ENTROPY OF TRANSITIVE MAPS OF THE INTERVAL

被引：4

作者：

COVEN, EM

HIDALGO, MC

机构：

[1] WESLEYAN UNIV,DEPT MATH,MIDDLETOWN,CT 06457

[2] UNIV HARTFORD,DEPT MATH,W HARTFORD,CT 06117

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 1991年 / 44卷 / 02期

关键词：

D O I：

10.1017/S0004972700029634

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The topological entropy of an continuous map of the interval is the suppremum of the topological entropies of the piecewise linear maps associated to its finite invariant sets. We show that for transitive maps, this supremum is attained at some finite invariant set if and only if the map is piecewise monotone and the set contains the endpoints of the interval and the turning points of the map.

引用

页码：207 / 213

页数：7

共 50 条

[1] TOPOLOGICAL-ENTROPY AND CHAOS OF INTERVAL MAPS
DU, BS
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1987, 11 (01) : 105 - 114
[2] CHAOS, TOPOLOGICAL-ENTROPY AND ALL TOPOLOGICALLY TRANSITIVE SUBSYSTEMS FOR SELF-MAPS OF THE INTERVAL
ZHOU, ZL
HUANG, XC
[J]. CHINESE SCIENCE BULLETIN, 1991, 36 (15): : 1315 - 1315
[3] Topological entropy of transitive maps of the interval
Block, Louis
Keesling, James
[J]. JOURNAL OF DIFFERENCE EQUATIONS AND APPLICATIONS, 2015, 21 (06) : 535 - 544
[4] ON TOPOLOGICAL-ENTROPY OF MAPS
HURLEY, M
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1995, 15 : 557 - 568
[5] A NOTE ON PERMUTATIONS AND TOPOLOGICAL-ENTROPY OF CONTINUOUS-MAPS OF THE INTERVAL
BYERS, B
[J]. CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES, 1986, 29 (01): : 91 - 95
[6] COMPUTING THE TOPOLOGICAL-ENTROPY OF MAPS OF THE INTERVAL WITH 3 MONOTONE PIECES
BLOCK, L
KEESLING, J
[J]. JOURNAL OF STATISTICAL PHYSICS, 1992, 66 (3-4) : 755 - 774
[7] COMPUTING THE TOPOLOGICAL-ENTROPY OF MAPS
COLLET, P
CRUTCHFIELD, JP
ECKMANN, JP
[J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1983, 88 (02) : 257 - 262
[8] MINIMAL PERIODIC-ORBITS AND TOPOLOGICAL-ENTROPY OF INTERVAL MAPS
DU, BS
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1987, 100 (03) : 482 - 484
[9] TOPOLOGICAL-ENTROPY FOR ANOSOV MAPS
SUN, WX
[J]. CHINESE SCIENCE BULLETIN, 1991, 36 (23): : 1948 - 1952
[10] VARIATION OF TOPOLOGICAL-ENTROPY IN A FAMILY OF PIECEWISE LINEAR UNIMODAL MAPS OF THE INTERVAL
BROUDISCOU, C
GILLOT, C
GILLOT, G
[J]. COMPTES RENDUS DE L ACADEMIE DES SCIENCES SERIE I-MATHEMATIQUE, 1985, 300 (16): : 585 - 588

← 1 2 3 4 5 →