Attractors and Chain Recurrence for Semigroup Actions

被引：39

作者：

Braga Barros, Carlos J. ^{[1
]}

Souza, Josiney A. ^{[1
]}

机构：

[1] Univ Estadual Maringa, Dept Matemat, BR-87020900 Maringa, Parana, Brazil

来源：

JOURNAL OF DYNAMICS AND DIFFERENTIAL EQUATIONS | 2010年 / 22卷 / 04期

关键词：

Limit sets; Attractors; Complementary repellers; Chain recurrence; SEMIFLOWS; SETS;

D O I：

10.1007/s10884-010-9164-3

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Let S be a semigroup acting on a topological space M. We define attractors for the action of S on M. This concept depends on a family F of subsets of S. For certain semigroups and families it recovers the concept of attractors for flows or semiflows. We define and study the complementary repeller of an attractor. We also characterize the set of chain recurrent points in terms of attractors.

引用

页码：723 / 740

页数：18

共 14 条

[1]

[Anonymous], 1978, Isolated invariant sets and the Morse index

[2]

[Anonymous], 1971, LECT TOPOLOGICAL DYN

[3] Chain transitive sets for flows on flag bundles [J].

Barros, Carlos J. Braga ;

San Martin, Luiz A. B. .

FORUM MATHEMATICUM, 2007, 19 (01) :19-60

[4]

Barros CJB, 1996, COMPUT APPL MATH, V15, P257

[5]

COLONIUS F, 1993, J DYN DIFFER EQU, V5, P495

[6]

Colonius F., 2000, SYS CON FDN

[7] THE GRADIENT STRUCTURE OF A FLOW .1. [J].

CONLEY, C .

ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1988, 8 :11-26

[8] The topological dynamics of semigroup actions [J].

Ellis, DB ;

Ellis, R ;

Nerurkar, M .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 2001, 353 (04) :1279-1320

[9]

Kelley John L., 1975, General topology

[10] MAXIMAL SUBSEMIGROUPS OF LIE-GROUPS THAT ARE TOTAL [J].

LAWSON, JD .

PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, 1987, 30 :479-501

← 1 2 →