Nicolae Lupa
Politehnica University of Timişoara, Timişoara, Romania

We generalize the classical concept of the evolution semigroup associated to an evolution family, replacing the usual right translation semiflow with a certain general real semiflow. We prove that under some suitable conditions, the evolution semigroup we consider is similar to the classical evolution semigroup. This enables us to apply well established results to completely characterize a wide class of dichotomies in terms of spectral conditions.