Abstract. The paper studies the robustness of a general notion of trichotomy, referred to as ``nonuniform $(h,k,\mu,\nu )$-trichotomy''. This means that any sufficiently small linear perturbation of a nonuniform $(h,k,\mu,\nu )$-trichotomy has the same asymptotic behavior as the original trichotomy. This result will be obtained as a consequence of two other important results: the robustness of dichotomy and the equivalence between a trichotomy and two dichotomies.

DOI: 10.14232/actasm-016-785-9

AMS Subject Classification (1991): 34D05, 34D09, 34D10, 93B35, 93C73

Keyword(s): dichotomy, trichotomy, robustness, evolution operator

Received July 13, 2016, and in revised form February 21, 2017. (Registered under 35/2016.)