Discrete Asymptotic Behaviors for Skew-Evolution Semiflows on Banach Spaces

Codruta Stoica (1) , Mihail Megan (2)

1 IMB - Institut de Mathématiques de Bordeaux
2 UVT - Faculte de Mathematiques

The paper emphasizes asymptotic behaviors, as stability, instability, dichotomy and trichotomy for skew-evolution semiflows, defined by means of evolution semiflows and evolution cocycles and which can be considered generalizations for evolution operators and skew-product semiflows. The definition are given in continuous time, but the unified treatment for the characterization of the studied properties in the nonuniform case is given in discrete time. The property of trichotomy, introduced in finite dimension by S. Elaydi and O. Hajek in 1988 as a natural generalization for the dichotomy of linear time-varying differential systems, was studied by us in continuous time and from uniform point of view and in discrete time and from nonuniform point of view but for a particular case of one-parameter semiflows.

Mots clés: Evolution semiflow; evolution cocycle; skew-evolution semiflow; exponential stability; exponential instability; exponential dichotomy; exponential trichotomy

Domaines: Analyse classique [math.CA]

Codruta Stoica, Mihail Megan. Discrete Asymptotic Behaviors for Skew-Evolution Semiflows on Banach Spaces. 2008. ⟨hal-00308877v2⟩