A generalization of Siegmund's normal forms theorem to systems with μ-dichotomies

2023/12/07 by Álvaro Castañeda, Castañeda, Álvaro, Néstor Jara +1 · 4 citations
Engineering · Mathematics · #34C20 #37C60 #37D25 #37G05 #Dynamical Systems (math.DS) #FOS: Mathematics #Mathematical Dynamics and Fractals #Stability and Controllability of Differential Equations #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2312.04544

openalex publication_date 2023/12/07 · openalex created_date 2023/12/09 · openalex updated_date 2026/07/28

Abstract

We establish a theorem concerning the normal forms by examining the newly presented concept of μ-dichotomy. This work establishes the nonresonance condition based on the associated spectrum of this general nonautonomous hyperbolicity.

Cited by

• Invariant foliations and linearization for partially hyperbolic nonautonomous dynamics
• C¹ Smoothness of the Conjugacy in a Delayed Nonautonomous Hartman--Grobman Theorem via μ-Dichotomies
• The interplay of μ-dichotomy, bounded growth, and spectral properties via growth rate comparisons
• Pugh's global linearization for the nonautonomous unbounded system with μ-dichotomy via Lyapunov theory

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