Smooth Linearization of Nonautonomous Differential Equations with a Nonuniform Dichotomy
Dynamical Systems
2019-12-11 v4
Abstract
In this paper we give a smooth linearization theorem for nonautonomous differential equations with a nonuniform strong exponential dichotomy. In terms of discretized evolution operator with hyperbolic fixed point 0, we formulate its spectrum and then give a spectral bound condition for the linearization of such equations to be simultaneously differentiable at 0 and H\"older continuous near 0. Restricted in the autonomous case, our result is the first one that gives a rigorous proof for simultaneously differentiable and H\"older linearization of hyperbolic systems without any non-resonant conditions.
Keywords
Cite
@article{arxiv.1902.06339,
title = {Smooth Linearization of Nonautonomous Differential Equations with a Nonuniform Dichotomy},
author = {Davor Dragicevic and Weinian Zhang and Wenmeng Zhang},
journal= {arXiv preprint arXiv:1902.06339},
year = {2019}
}
Comments
Final version incorporating comments from the referees. Accepted for publication in Proceedings of the London Mathematical Society