Differentiability of Palmer's linearization Theorem and converse result for density functions
Classical Analysis and ODEs
2015-12-07 v2 Dynamical Systems
Abstract
We study differentiability properties in a particular case of the Palmer's linearization Theorem, which states the existence of an homeomorphism between the solutions of a linear ODE system having exponential dichotomy and a quasilinear system. Indeed, if the linear system is uniformly asymptotically stable, sufficient conditions ensuring that is a preserving orientation diffeomorphism are given. As an application, we generalize a converse result of density functions for a nonlinear system in the nonautonomous case.
Keywords
Cite
@article{arxiv.1406.5492,
title = {Differentiability of Palmer's linearization Theorem and converse result for density functions},
author = {Alvaro Castañeda and Gonzalo Robledo},
journal= {arXiv preprint arXiv:1406.5492},
year = {2015}
}