Trichotomy for Dynamical Systems in Banach Spaces

We construct a framework for the study of dynamical systems that describe phenomena from physics and engineering in infinite dimensions and whose state evolution is set out by skew-evolution semiflows. Therefore, we introduce the concept of ω-trichotomy. Characterizations in a uniform setting are proved, using techniques from the domain of nonautonomous evolution equations with unbounded coefficients, and connections with the classic notion of trichotomy are given. The statements are sustained by several examples.