2025/01/11 by Davor Dragičević, Dragicevic, Davor, César M. Silva +1 · 2 citations
Mathematics · #Classical Analysis and ODEs (math.CA) #Dynamical Systems (math.DS) #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Nonlinear Differential Equations Analysis
paper · doi:10.48550/arxiv.2501.06630
openalex publication_date 2025/01/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
For discrete-time nonautonomous linear dynamics and a large class of discrete growth rates μ, we show that the notion of μ dichotomy (with respect to a sequence of norms) can be completely characterized in terms of ordinary and exponential dichotomy (with respect to a sequence of norms) by employing a suitable rescaling of time. Previously, such a result was known only in the particular case of polynomial dichotomies. As a nontrivial application of our results, we study the structure of a generalized Sacker-Sell spectrum and obtain a series of nonautonomous topological and smooth linearization results.