Generalized dichotomies via time rescaling
Dynamical Systems
2026-05-05 v2 Classical Analysis and ODEs
Abstract
For discrete-time nonautonomous linear dynamics and a large class of discrete growth rates , we show that the notion of 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.
Cite
@article{arxiv.2501.06630,
title = {Generalized dichotomies via time rescaling},
author = {Davor Dragicevic and Cesar M. Silva},
journal= {arXiv preprint arXiv:2501.06630},
year = {2026}
}