Smoothness of topological equivalence on the half line for nonautonomous systems

We study the differentiability properties of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable nonlinearities. For this purpose, we construct a homeomorphism inspired in the Palmer's one restricted to the posit...

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Bibliographic Details
Published in:Proceedings of the Royal Society of Edinburgh. Section A. Mathematics 2020-10, Vol.150 (5), p.2484-2502
Main Authors: Castañeda, Álvaro, Robledo, Gonzalo, Monzón, Pablo
Format: Article
Language:English
Subjects:
Equivalence
Smoothness
Topology
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Summary:We study the differentiability properties of the topological equivalence between a uniformly asymptotically stable linear nonautonomous system and a perturbed system with suitable nonlinearities. For this purpose, we construct a homeomorphism inspired in the Palmer's one restricted to the positive half line, studying additional continuity properties and providing sufficient conditions ensuring its Cr–smoothness.
ISSN:0308-2105
1473-7124
DOI:10.1017/prm.2019.32