Structural stability of evolution families in finite-dimensional spaces

We prove that under some appropriate conditions, exponential dichotomy of an evolution family is implied by a weaker concept of structural stability . We extend precedent results, which are only valid in the case of differential equations with bounded operators. In addition, we establish new characterizations of exponential stability and exponential expansiveness, in terms of topological equivalence. Our proofs are new even in the particular case of differential equations.