Nonautonomous equations and almost reducibility sets

For a nonautonomous differential equation, we consider the almost reducibility property that corresponds to the reduction of the original equation to an autonomous equation via a coordinate change preserving the Lyapunov exponents. In particular, we characterize the class of equations to which a giv...

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Bibliographic Details
Main Authors: Barreira Luis
Valls Claudia
Format: Serial
Published: 2021
Series:Electronic journal of qualitative theory of differential equations
Kulcsszavak:Differenciálegyenlet
doi:10.14232/ejqtde.2021.1.11

Online Access:http://acta.bibl.u-szeged.hu/73663
Description
Summary:For a nonautonomous differential equation, we consider the almost reducibility property that corresponds to the reduction of the original equation to an autonomous equation via a coordinate change preserving the Lyapunov exponents. In particular, we characterize the class of equations to which a given equation is almost reducible. The proof is based on a characterization of the almost reducibility to an autonomous equation with a diagonal coefficient matrix. We also characterize the notion of almost reducibility for an equation x 0 = A(t, θ)x depending continuously on a real parameter θ. In particular, we show that the almost reducibility set is always an Fσδ-set and for any Fσδ-set containing zero we construct a differential equation with that set as its almost reducibility set.
Physical Description:14
ISSN:1417-3875