Abstract
For a one-sided nonautonomous dynamics defined by a sequence of linear operators, we obtain a complete characterization of (strong) nonuniform exponential contractions and (strong) nonuniform exponential expansions in terms of admissibility of certain pairs of sequence spaces. We allow asymptotic rates of the form \({e^{c\rho(n)}}\) determined by an arbitrary increasing sequence \({\rho(n)}\) that tends to infinity. For example, the usual exponential behavior with \({\rho(n) = n}\) is included as a very special case. As a nontrivial application of our work, we establish the robustness of (strong) nonuniform exponential contractions and (strong) nonuniform exponential expansions, that is, the persistence of those notions under sufficiently small linear perturbations.
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Luis Barreira and Claudia Valls were supported by FCT/Portugal through UID/MAT/04459/2013. Davor Dragičević was supported in part by an Australian Research Council Discovery Project DP150100017, Croatian Science Foundation under the Project IP-2014-09-2285 and by the University of Rijeka Research Grant 13.14.1.2.02.
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Barreira, L., Dragičević, D. & Valls, C. Characterization of Nonuniform Contractions and Expansions with Growth Rates. Mediterr. J. Math. 13, 4265–4279 (2016). https://doi.org/10.1007/s00009-016-0744-2
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DOI: https://doi.org/10.1007/s00009-016-0744-2