SPECTRAL CONDITIONS FOR A DICHOTOMY

MARCOS LIZANA AND JAMES MULDOWNEY

Abstract. We consider a linear system of differential equations x' = A(t)x where A(t) is bounded, continuous and slowly varying. It is shown that, if the spectrum of A(t) is separated in a certain averaged sense in the complex plane, there is an invariant splitting of the solution space into subspaces for which elements of the spectrum furnish bounds on the growth rate of the solutions.