Admissibility and general dichotomies for evolution families

2020/02/08 by Dragicevic, Davor, Pecek, Nevena Jurcevic, Lupa, Nicolae · 1 citation
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.2002.03202

Abstract

For an arbitrary noninvertible evolution family on the half-line and for ρ\colon [0, ∞)→ [0, ∞) in a large class of rate functions, we consider the notion of a ρ-dichotomy with respect to a family of norms and characterize it in terms of two admissibility conditions. In particular, our results are applicable to exponential as well as polynomial dichotomies with respect to a family of norms. As a nontrivial application of our work, we establish the robustness of general nonuniform dichotomies.

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