Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
1891334 | Chaos, Solitons & Fractals | 2016 | 8 Pages |
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(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 ZZ. Finally, we use the former characterizations to establish the robustness of the notion of a nonuniform exponential dichotomy.
Keywords
Related Topics
Physical Sciences and Engineering
Physics and Astronomy
Statistical and Nonlinear Physics
Authors
Luis Barreira, Davor Dragičević, Claudia Valls,