Barreira Luis and Valls Claudia: Nonautonomous equations and almost reducibility sets. (2021)
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Abstract
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.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2021 |
| Number: | 11 |
| ISSN: | 1417-3875 |
| Number of Pages: | 14 |
| Language: | English |
| DOI: | 10.14232/ejqtde.2021.1.11 |
| Uncontrolled Keywords: | Differenciálegyenlet |
| Additional Information: | Bibliogr.: 14. p. ; összefoglalás angol nyelven |
| Date Deposited: | 2021. Nov. 08. 09:44 |
| Last Modified: | 2021. Nov. 08. 09:44 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/73663 |
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