On Roughness of Exponential Dichotomy

We present new perturbation theorems on the roughness of exponential dichotomy, which improve previous results. The proofs given here are also much simpler compared with previous ones. The new results provide significant improvements of existing results in the case where the operator A t is unbounded for t ∈ J. This is precisely the situation that is of interest from the point of view of the applications in lobe dynamics. The results are also valid in Banach spaces and useful for general purposes