Algebraic transition matrices in the Conley index theory

被引：10

作者：

Franzosa, R ^{[1
]}

Mischaikow, K

机构：

[1] Univ Maine, Dept Math, Orono, ME 04469 USA

[2] Georgia Inst Technol, Sch Math, Ctr Dynam Syst & Nonlinear Studies, Atlanta, GA 30322 USA

[3] Univ Sao Paulo, Inst Ciencias Math Sao Carlo, BR-05508 Sao Paulo, Brazil

来源：

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1998年 / 350卷 / 03期

关键词：

Conley index; connection matrix; transition matrix; bistable attractor; travelling waves;

D O I：

10.1090/S0002-9947-98-01666-3

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We introduce the concept of an algebraic transition matrix. These are degree zero isomorphisms which are upper triangular with respect to a partial order. It is shown that all connection matrices of a Morse decomposition for which the partial order is a series-parallel admissible order are related via a conjugation with one of these transition matrices. This result is then restated in the form of an existence theorem for global bifurcations. Simple examples of how these results can be applied are also presented.

引用

页码：889 / 912

页数：24

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