Fredholm operators and nonuniform exponential dichotomies

Luis Barreira, Davor Dragičević and Claudia Valls

Chaos, Solitons & Fractals, 2016, vol. 85, issue C, 120-127

Abstract: We show that the existence of a nonuniform exponential dichotomy for a one-sided sequence (Am)m ≥ 0 of invertible d × d matrices is equivalent to the Fredholm property of a certain linear operator between spaces of bounded sequences. Moreover, for a two-sided sequence (Am)m∈Z we show that the existence of a nonuniform exponential dichotomy implies that a related operator S is Fredholm and that if it is Fredholm, then the sequence admits nonuniform exponential dichotomies on Z0+ and Z0−. We also give conditions on S so that the sequence admits a nonuniform exponential dichotomy on Z. Finally, we use the former characterizations to establish the robustness of the notion of a nonuniform exponential dichotomy.

Keywords: Exponential dichotomies; Robustness; Fredholm operators (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:85:y:2016:i:c:p:120-127

DOI: 10.1016/j.chaos.2016.01.021

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