Connections between Some Concepts of Polynomial Trichotomy for Noninvertible Evolution Operators in Banach Spaces

Abstract

The present paper treats three concepts of nonuniform polynomial trichotomies for noninvertible evolution operators acting on Banach spaces. The connections between these concepts are established through numerous examples and counterexamples for systems defined on the Banach space of square-summable sequences.

On some dichotomy concepts with different growth rates for evolution operators in Banach spaces

“…In the case in which h(t) = k(t) = N (t) = t + 1 then we get a study of the nonuniform polynomial dichotomy concepts, studied in [2]. The polynomial framework was extended to the trichotomy case, and it was done in [1]. The exponential case, in which h(t) = k(t) = N (t) = e t was treated, for example, in [3].…”

On uniform polynomial trichotomy of skew-evolution semiflows

“…Also, we remark the results obtained by P. V. Hai ([12]) for the polynomial stability, using techniques of Banach function spaces. Regarding more general properties of nonuniform polynomial trichotomy, in [1], the authors consider three concepts of polynomial trichotomy for evolution operators and emphasize interesting examples, respectively counterexamples.…”