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Exponential trichotomy of differential systems. (English) Zbl 0651.34052

The notion of exponential trichotomy, which is due to Elaydi and Hajek in an earlier paper, is a natural generalisation of that of exponential dichotomy which is familiar in stability questions for dynamical systems. It is stronger than the notion of trichotomy introduced by Sacker and Sell in 1976. It is shown that an upper triangular system possesses an exponential trichotomy if and only if its diagonal process does. If a linear system has an exponential trichotomy then certain stability results for small nonlinear perturbations of the linear system are established.
Reviewer: J.F.Toland

MSC:

34D10 Perturbations of ordinary differential equations
34D05 Asymptotic properties of solutions to ordinary differential equations
34A30 Linear ordinary differential equations and systems
34A34 Nonlinear ordinary differential equations and systems
37-XX Dynamical systems and ergodic theory
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References:

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