Abstract
This paper focuses on the linear perturbation of dynamical systems in Banach spaces, which corresponds to a nonautonomous dynamical system admitting a nonuniform ( μ , ν ) -dichotomy. We establish the robustness or roughness of nonuniform ( μ , ν ) -dichotomies, in the sense that the linear dynamical system persists under a sufficiently small linear perturbation.
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