Smoothness of Topological Equivalence on the Half Line for Nonautonomous Systems
Abstract
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 uniformly continuous homeomorphism inspired in the Palmer's one restricted to the positive half line, providing sufficient conditions ensuring its Cr--smoothness. Additionally, we study the preservation of the uniform stability properties by this homeomorphism.
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