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This paper focuses on a new notion called the general exponential dichotomy on time scales, which is more general and contains as special cases most versions of dichotomies on the continuous systems and discrete systems. We establish the existence of parameter dependence of roughness for the general exponential dichotomy on time scales under sufficiently small linear perturbation. Moreover, we also show that the stable and unstable subspaces of general exponential dichotomies for the perturbed system are Lipschitz continuous for the parameters.

General exponential dichotomies on time scales and parameter dependence of roughness