Robustness of nonuniform -dichotomies in Banach spaces

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.