A zero topological entropy map for which periodic points are not a Gδ set

被引：2

作者：

Sindelárová, P ^{[1
]}

机构：

[1] Silesian Univ, Math Inst, Opava 74601, Czech Republic

来源：

ERGODIC THEORY AND DYNAMICAL SYSTEMS | 2002年 / 22卷

关键词：

D O I：

10.1017/S0143385702000494

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We exhibit an example of a continuous map of the interval of type 2(infinity), and hence of zero topological entropy, for which the set of periodic points is not a G(delta) set. This disproves a conjecture by Sharkovsky from 1965. Unfortunately, this conjecture has been incorrectly quoted as a true statement by other authors in many papers and books.

引用

页码：947 / 949

页数：3

共 13 条

[1] STABILITY OF PERIODIC-ORBITS IN THE THEOREM OF SARKOVSKII
BLOCK, L
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1981, 81 (02) : 333 - 336
[2] COLLET P, 1980, ITERATED MAPS INTERV
[3] DEMELO W, 1993, ONE DIMENSIONAL DYNA
[4] CHARACTERIZATIONS OF WEAKLY CHAOTIC MAPS OF THE INTERVAL
FEDORENKO, VV
SARKOVSKII, AN
SMITAL, J
[J]. PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1990, 110 (01) : 141 - 148
[5] ON DYNAMICS OF TRIANGULAR MAPS OF THE SQUARE
KOLYADA, SF
[J]. ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1992, 12 : 749 - 768
[6] ABSOLUTELY CONTINUOUS MEASURES FOR CERTAIN MAPS OF AN INTERVAL
MISIUREWICZ, M
[J]. PUBLICATIONS MATHEMATIQUES DE L IHES, 1981, (53): : 17 - 51
[7] SHARKOVSKII AN, 1968, UKR MAT ZH, V20, P136
[8] SHARKOVSKII AN, 1965, UKRAIN MATH ZH, V17, P104, DOI DOI 10.1007/BF02527365
[9] Sharkovsky A. N., 1993, DIFFERENCE EQUATIONS
[10] SHARKOVSKY AN, 1997, DYNAMICS ONE DIMENSI

← 1 2 →