Lyapunov functions for strong exponential dichotomies (CROSBI ID 188014)
Prilog u časopisu | izvorni znanstveni rad | međunarodna recenzija
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