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Lyapunov functions for strong exponential dichotomies (CROSBI ID 188014)

Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija

Barreira, Luis ; Dragičević, Davor ; Valls, Claudia Lyapunov functions for strong exponential dichotomies // Journal of mathematical analysis and applications, 399 (2013), 1; 116-132. doi: 10.1016/j.jmaa.2012.10.004

Podaci o odgovornosti

Barreira, Luis ; Dragičević, Davor ; Valls, Claudia

engleski

Lyapunov functions for strong exponential dichotomies

We give a complete characterization of a general type of exponential dichotomies in terms of Lyapunov functions, both for discrete and continuous time. This includes constructing explicitly quadratic Lyapunov functions for each exponential dichotomy. We consider the general cases of nonautonomous dynamics, nonuniform exponential dichotomies and, motivated by ergodic theory, strong exponential dichotomies, in the sense that there exist simultaneously lower and upper contraction and expansion bounds. As a nontrivial application, we establish the persistence of the asymptotic stability of a strong nonuniform exponential dichotomy under sufficiently small linear perturbations.

exponential dichotomies ; Lyapunov functions ; robustness

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Podaci o izdanju

399 (1)

2013.

116-132

objavljeno

0022-247X

1096-0813

10.1016/j.jmaa.2012.10.004

Povezanost rada

Matematika

Poveznice
Indeksiranost