Geodesic
Floquet problem and center manifold reduction for ordinary differential operators with periodic coefficients in Hilbert spaces
Algebra i analiz, Tome 32 (2020) no. 3, pp. 191-218.

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A first order differential equation with a periodic operator coefficient acting in a pair of Hilbert spaces is considered. This setting models both elliptic equations with periodic coefficients in a cylinder and parabolic equations with time periodic coefficients. Our main results are a construction of a pointwise projector and a spectral splitting of the system into a finite-dimensional system of ordinary differential equations with constant coefficients and an infinite dimensional part whose solutions have better properties in a certain sense. This complements the well-known asymptotic results for periodic hypoelliptic problems in cylinders and for elliptic problems in quasicylinders obtained by P. Kuchment and S. A. Nazarov, respectively. As an application we give a center manifold reduction for a class of nonlinear ordinary differential equations in Hilbert spaces with periodic coefficients. This result generalizes the known case with constant coefficients explored by A. Mielke.
Keywords: Floquet theorem, differential equations with periodic coefficients, asymptotics of solutions to differential equations, center manifold reduction. 
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     title = {Floquet problem and center manifold reduction for ordinary differential operators with periodic coefficients in {Hilbert} spaces},
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     url = {http://geodesic.mathdoc.fr/item/AA_2020_32_3_a8/}
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V. Kozlov; J. Taskinen. Floquet problem and center manifold reduction for ordinary differential operators with periodic coefficients in Hilbert spaces. Algebra i analiz, Tome 32 (2020) no. 3, pp. 191-218. http://geodesic.mathdoc.fr/item/AA_2020_32_3_a8/

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