Nonuniform dichotomies via time rescaling
Abstract
We establish characterizations of general nonuniform dichotomies for linear nonautonomous dynamical systems in terms of nonuniform exponential dichotomies of appropriately time-rescaled systems. In discrete time, for a class of slowly growing rates, such a characterization requires an additional condition involving a suitable notion of nonuniform ordinary dichotomy, which can be omitted for invertible systems. In continuous time, we obtain a more general characterization for a large class of growth rates, without imposing this additional condition. Our approach does not rely on adapted Lyapunov norms and applies to evolution families on arbitrary Banach spaces. As applications, we show how several results concerning general nonuniform dichotomies can be derived from their counterparts for exponential dichotomies.
Related
- h-dichotomies via noncritical uniformity and expansiveness for noninvertible evolution families
- Admissible characterization in delay equations and robustness of exponential dichotomies against small-delay perturbations
- Channel dichotomies
- Adjoint Transfer and Order-Lifting Dichotomies for 2 x 2 Matrices over Prime-Power Rings
- Chow Quotient Moduli Space of Dynamical Systems on the Projective Line and Rescaling Limits
BibTeX
@misc{dragicevic2026nonuniform,
title = {{Nonuniform dichotomies via time rescaling}},
author = {Davor Dragicevic and Cesar M. Silva},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18329},
eprint = {2610.18329},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18329},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Nonuniform dichotomies via time rescaling
AU - Davor Dragicevic
AU - Cesar M. Silva
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18329
UR - https://arxiv.org/abs/2610.18329
AB - We establish characterizations of general nonuniform dichotomies for linear nonautonomous dynamical systems in terms of nonuniform exponential dichotomies of appropriately time-rescaled systems. In discrete time, for a class of slowly growing rates, such a characterization requires an additional condition involving a suitable notion of nonuniform ordinary dichotomy, which can be omitted for invertible systems. In continuous time, we obtain a more general characterization for a large class of growth rates, without imposing this additional condition. Our approach does not rely on adapted Lyapunov norms and applies to evolution families on arbitrary Banach spaces. As applications, we show how several results concerning general nonuniform dichotomies can be derived from their counterparts for exponential dichotomies.
ER -