Existence and robustness of nonuniform (h,k,μ,ν)-dichotomies for nonautonomous impulsive differential equations

For the linear nonautonomous impulsive differential equation, we propose a new notion called the nonuniform (h,k,μ,ν)-dichotomy, which extends the notion of dichotomy of uniform and nonuniform types and is related to the theory of nonuniform hyperbolicity. We establish a sufficient criterion for the existence of the nonuniform (h,k,μ,ν)-dichotomy in terms of appropriate Lyapunov exponents. For the linear perturbation, we develop the robustness or roughness of nonuniform (h,k,μ,ν)-dichotomies in the sense that a nonuniform (h,k,μ,ν)-dichotomy persists under a sufficiently small linear perturbation.