Lyapunov's second method for nonautonomous differential equations

被引：0
作者：
Gruene, Lars
Kloeden, Peter E.
Siegmund, Stefan
Wirth, Fabian R.
机构：
[1] Univ Bayreuth, Inst Math, D-95440 Bayreuth, Germany
[2] Univ Frankfurt, Inst Comp Orientierte Math, D-60054 Frankfurt, Germany
[3] Natl Univ Ireland Maynooth, Hamilton Inst, Maynooth, Kildare, Ireland
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2007年 / 18卷 / 2-3期
关键词：
lyapunov function; Lyapunov's second method; nonautonomous dynamical system; nonautonomous differential equation; stability; nonautonomous attractor;
D O I：
暂无
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
Converse Lyapunov theorems are presented for nonautonomous systems modelled as skew product flows. These characterize various types of stability of invariant sets and pullback, forward and uniform attractors in such nonautonomous systems.
引用
收藏
页码：375 / 403
页数：29
相关论文
共 31 条
[1]  
Amann H., 1990, GRUYTER STUDIES MATH, V13
[2]  
[Anonymous], 1966, PUBLICATIONS MATH SO
[3]  
[Anonymous], 1967, STABILITY MOTION
[4]   Lyapunov's second method for random dynamical systems [J].
Arnold, L ;
Schmalfuss, B .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2001, 177 (01) :235-265
[5]   On the Gap Between Random Dynamical Systems and Continuous Skew Products [J].
Arno Berger ;
Stefan Siegmund .
Journal of Dynamics and Differential Equations, 2003, 15 (2-3) :237-279
[6]  
Bhatia N. P., 1970, CLASSICS MATH
[7]  
Bronstein I.U., 1994, SMOOTH INVARIANT MAN
[8]   A generalization of Zubov's method to perturbed systems [J].
Camilli, F ;
Grüne, L ;
Wirth, F .
SIAM JOURNAL ON CONTROL AND OPTIMIZATION, 2001, 40 (02) :496-515
[9]   THE GRADIENT STRUCTURE OF A FLOW .1. [J].
CONLEY, C .
ERGODIC THEORY AND DYNAMICAL SYSTEMS, 1988, 8 :11-26
[10]  
Conley C., 1978, CBMS REGIONAL C SERI, V38
1234