Equicontinuity of a graph map

被引：9

作者：

Sun, TX ^{[1
]}

Zhang, YP ^{[1
]}

Zhang, XY ^{[1
]}

机构：

[1] Guangxi Univ, Dept Math, Nanning 530004, Guangxi, Peoples R China

来源：

BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY | 2005年 / 71卷 / 01期

关键词：

D O I：

10.1017/S0004972700038016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Let G be a graph, and f : G -> G be a continuous map with periodic points. In this paper we show that the following five statements are equivalent. (1) f is equicontinuous. (2) There exists some positive integer N such that f N is uniformly convergent. (3) f is S-equicontinuous for some positive integer sequence S = {n(1) < n(2) < (...)}. (4) Omega(x,f) =w(x,f) for every x epsilon G. (5) sigma : (lim) under left arrow {X, f} -> (lim) under left arrow {X, f} is a periodic map.

引用

页码：61 / 67

页数：7

共 13 条

[1]

Akin E, 1996, OHIO ST U M, V5, P25

[2] LINEAR-ORDERINGS AND THE FULL PERIODICITY KERNEL FOR THE N-STAR [J].

ALSEDA, L ;

MORENO, JM .

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 1993, 180 (02) :599-616

[3] Topological complexity [J].

Blanchard, F ;

Host, B ;

Maass, A .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 2000, 20 :641-662

[4] THE SET OF ALL ITERATES IS NOWHERE DENSE IN C([0, 1], [0, 1]) [J].

BLOKH, AM .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1992, 333 (02) :787-798

[5] GAMMA-COMPACT MAPS ON AN INTERVAL AND FIXED POINTS [J].

BOYCE, WM .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1971, 160 (NOCT) :87-&

[6]

BRUCKNER AM, 1990, TAMKANG J MATH, V21, P287

[7] COMMON FIXED-POINTS FOR A CLASS OF COMMUTING MAPPINGS ON AN INTERVAL [J].

CANO, J .

PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY, 1982, 86 (02) :336-338

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

Mai, JH .

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

[9]

NADLER SB, 1992, CONTINUUM THEORY PUR, V158

[10]

Qiao, 2001, SE ASIAN B MATH, V25, P413

← 1 2 →