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Multiscale linearization of nonautonomous systems

Part of: Stability theory

Published online by Cambridge University Press:  23 September 2022

Lucas Backes  and
Davor Dragičević
Lucas Backes
Affiliation:
Departamento de Matemática, Universidade Federal do Rio Grande do Sul, Av. Bento Gonçalves 9500, CEP 91509-900, Porto Alegre, RS, Brazil ([email protected])
Davor Dragičević
Affiliation:
Faculty of Mathematics, University of Rijeka, Croatia ([email protected])
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Abstract

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.

Keywords

Multiscalelinearizationnonautonomous dynamics

MSC classification

Primary: 34D30: Structural stability and analogous concepts
Secondary: 34D09: Dichotomy, trichotomy
Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 153 , Issue 5 , October 2023 , pp. 1609 - 1629
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Copyright
Copyright © The Author(s), 2022. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh

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