C¹ Smoothness of the Conjugacy in a Delayed Nonautonomous Hartman--Grobman Theorem via μ-Dichotomies

2025/08/21 by Álvaro Castañeda, Castañeda, Álvaro, Heli Elorreaga +1
Engineering · Mathematics · #34D09 #34k06 #34k20 #34k27 #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Differential Equations Analysis #Stability and Control of Uncertain Systems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2508.15696

openalex publication_date 2025/08/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We investigate the differentiability of the conjugacy in a nonautonomous version of the Hartman--Grobman Theorem for systems with finite delay, where the linear part satisfies a μ-dichotomy. Under suitable conditions on the nonlinear perturbation, the conjugacy is shown to be a C¹ diffeomorphism.

Citations

• Spectrum invariance dilemma for nonuniformly kinematically similar systems
• A generalization of Siegmund's normal forms theorem to systems with μ-dichotomies

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