Dichotomies Faster or Slower than exponential are Irrelevant for Skew-Product Flows

We prove that dichotomies given by growth rates that are either faster or slower than exponential either do not occur or are inconsequential in the setting of skew-products with compact base. A similar conclusion is obtained for the nonuniform exponential behavior. To achieve this, we study families of translated linear nonautonomous differential equations for which we prove propagation results. We also study translations of growth rates under a comparison criteria.