A Floquet-Liapunov theorem in Fréchet spaces
نویسندگان
چکیده
Based on [4], we prove a variation of the theorem in title, for equations with periodic coefficients, in Fréchet spaces. The main result gives equivalent conditions ensuring the reduction of such an equation to one with constant coefficient. In the particular case of C ∞ , we obtain the exact analogue of the classical theorem. Our approach essentially uses the fact that a Fréchet space is the limit of a projective sequence of Banach spaces. This method can also be applied for a geometric interpretation of the same theorem within the context of total differential equations in Fréchet fiber bundles.
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