RELATIVELY POINTWISE RECURRENT GRAPH MAP

被引：2

作者：

Hawete, Hattab ^{[1
]}

机构：

[1] Inst Super Informat & Multimedia, Sfax 3021, Tunisia

来源：

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY | 2011年 / 139卷 / 06期

关键词：

Periodic point; recurrent point; almost periodic point; minimal set; relatively pointwise recurrent map; graph map; PERIODIC HOMEOMORPHISMS;

D O I：

10.1090/S0002-9939-2010-10622-6

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let f be a self-continuous map of a graph G. Let P(f) and R(f) denote the sets of periodic points and recurrent points respectively. We say that the map f is relatively recurrent if <(R(f))over bar> = G. In this paper, it is shown that f is relatively recurrent if and only if one of the following statements holds: (a) G is a circle and f is a homeomorphism topologically conjugate to an irrational rotation of the unit circle S-1; (b) <(P(f))over bar> = G. Part (b) extends a result of Blokh.

引用

页码：2087 / 2092

页数：6

共 15 条

[1]

[Anonymous], 1944, Bull. Amer. Math. Soc., DOI DOI 10.1090/S0002-9904-1944-08115-9

[2]

[Anonymous], 1981, MB PORTER LECT

[3] Minimal sets on graphs and dendrites [J].

Balibrea, F ;

Hric, R ;

Snoha, L .

INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2003, 13 (07) :1721-1725

[4]

Birkhoff G.D, 1966, Amer. Math. Soc. Colloq. Publ., VIX

[5] ON THE CONNECTION BETWEEN ENTROPY AND TRANSITIVITY FOR ONE-DIMENSIONAL MAPPINGS [J].

BLOKH, AM .

RUSSIAN MATHEMATICAL SURVEYS, 1987, 42 (05) :165-166

[6]

EPSTEIN DBA, 1981, P LOND MATH SOC, V42, P415

[7]

Hasselblatt B., 2003, 1 COURSE DYNAMICS PA

[8]

Illanes A., 1998, TOPOLOGY P, V23, P221

[9] Pointwise-recurrent graph maps [J].

Mai, JH .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2005, 25 :629-637

[10] The structure of equicontinuous maps [J].

Mai, JH .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2003, 355 (10) :4125-4136

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