Exponential dichotomies of linear dynamic equations on measure chains under slowly varying coefficients. (Q1419783)

The author presents a theorem on robustness of exponential dichotomies for linear dynamic equations within a very general framework: The equations are modelled on so-called measure chains, which cover ordinary differential equations, ordinary difference equations and many other types of time scales. Further on, the state space may be infinite-dimensional, the linear maps are not assumed to be invertible. Also, the dependence on a slowly varying parameter from a metric space is considered. The notions and proofs are quite technical, nevertheless the author presents the theory in a clear and consistent way.