Existence and roughness of exponential dichotomies of linear dynamic equations on time scales

In this paper, we define the exponential dichotomy of linear dynamic equations on time scales, then we present perturbation theorems on the roughness of exponential dichotomy, and develop several explicit sufficient criteria for linear dynamic equations to have an exponential dichotomy. As applications of the criteria of exponential dichotomy, we derive some new sufficient conditions for the existence of periodic solutions of semi-linear dynamic equations and nonlinear dynamic equations on time scales.