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Exponential dichotomy of nonautonomous periodic systems in terms of the boundedness of certain periodic Cauchy problems. (English) Zbl 1294.34059
The author considers exponential dichotomy of nonautonomous periodic systems in terms of the boundedness of certain periodic Cauchy problems. He presents a sufficient and necessary condition that a family of \(q\)-periodic continuous matrix valued function \(\{A(t)\}_{t\in\mathbb R}\) has an exponential dichotomy with a projector \(P\).

MSC:
34D09 Dichotomy, trichotomy of solutions to ordinary differential equations
47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.)
34C11 Growth and boundedness of solutions to ordinary differential equations
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