Linearization of a nonautonomous unbounded system with nonuniform contraction: A Spectral Approach
Classical Analysis and ODEs
2020-01-13 v2
Abstract
For a nonautonomous linear system with nonuniform contraction, we construct a topological equivalence between this system and an unbounded nonlinear perturbation. This topological equivalence is constructed as a composition of homeomorphisms. The first one is set up by considering the fact that linear system is almost reducible to diagonal system with a small enough perturbation where the diagonal entries belong to spectrum of the nonuniform exponential dichotomy; and the second one is constructed in terms of the crossing times with respect to unit sphere of an adequate Lyapunov function associated to the linear system.
Keywords
Cite
@article{arxiv.1905.07319,
title = {Linearization of a nonautonomous unbounded system with nonuniform contraction: A Spectral Approach},
author = {I. Huerta},
journal= {arXiv preprint arXiv:1905.07319},
year = {2020}
}