Lyapunov's second method for nonautonomous differential equations

L. Grüne, P.E. Kloeden, S. Siegmund, F. Wirth: Lyapunov's second method for nonautonomous differential equations
Discrete and Continuous Dynamical Systems - Series A 18 (Special Issue on Nonautonomous, Stochastic and Hamiltonian Dynamical Systems), 375 - 403, 2007

DOI: 10.3934/dcds.2007.18.375
Keywords: stability; Lyapunov's direct method; nonautonomous differential equations; converse Lyapunov theorems; skew product flows; attractors
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Abstract:

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.

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