Multiscale linearization of nonautonomous systems

Multiscale linearization of nonautonomous systems

We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are well-behaved, we do not assume any asymptotic behaviour of the lin...

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Veröffentlicht in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2023-10, Vol.153 (5), p.1609-1629
Hauptverfasser: Backes, Lucas, Dragičević, Davor
Format: Artikel
Sprache:eng
Schlagworte:
Asymptotic properties
Banach spaces
Decomposition
Nonlinear control
Perturbation
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Zusammenfassung:We present sufficient conditions under which a given linear nonautonomous system and its nonlinear perturbation are topologically conjugated. Our conditions are of a very general form and provided that the nonlinear perturbations are well-behaved, we do not assume any asymptotic behaviour of the linear system. Moreover, the control on the nonlinear perturbations may differ along finitely many mutually complementary directions. We consider both the cases of one-sided discrete and continuous dynamics.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2022.63