Nonuniform exponential dichotomies and Fredholm operators for flows. (English) Zbl 1373.37080
Since the work of K. J. Palmer [J. Differ. Equations 55, 225–256 (1984; Zbl 0508.58035); Proc. Am. Math. Soc. 104, No. 1, 149–156 (1988; Zbl 0675.34006)], it is well known that there exists a close relationship between exponential dichotomies of linear differential equations \(\dot x=A(t)x\) and Fredholm properties of an operator \((Lx)(t):=\dot x(t)-A(t)x\) between ambient function spaces. The authors obtain corresponding results when dealing with their (strong) nonuniform exponential dichotomy, both for equations on halflines, as well as the entire real axis. As a consequence, roughness results for dichotomies are derived.
Reviewer: Christian Pötzsche (Klagenfurt)
MSC:
| 37C60 | Nonautonomous smooth dynamical systems |
| 34D09 | Dichotomy, trichotomy of solutions to ordinary differential equations |
| 47A13 | Several-variable operator theory (spectral, Fredholm, etc.) |
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