Global asymptotic stability for differentiable vector fields of R2

被引：41
作者：
Fernandes, A
Gutierrez, C
Rabanal, R
机构：
[1] Univ Sao Paulo, Inst Ciencias Matemat & Comp, BR-13560970 Sao Carlos, SP, Brazil
[2] Univ Fed Ceara, Dept Matemat, BR-60455760 Fortaleza, Ceara, Brazil
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2004年 / 206卷 / 02期
关键词：
planar vector fields; global injectivity; asymptotic stability;
D O I：
10.1016/j.jde.2004.04.015
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
(a) Let X: R-2 --> R-2 be a differentiable map (not necessarily C-1) and let Spec(X) be the set of (complex) eigenvalues of the derivative DXp when p varies in R-2. If, for some epsilon > 0, Spec(X) boolean AND [0, epsilon) = phi then X is injective. (b) Let X: R-2 --> R-2 be a differentiable vector field such that X(0) = 0 and Spec(X) subset of {z is an element of C : R(z) < 0}. Then, for all p is an element of R-2, there is a unique positive trajectory starting at p; moreover the omega-limit set of p is equal to {0}. (C) 2004 Elsevier Inc. All rights reserved.
引用
收藏
页码：470 / 482
页数：13
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