A Global Hartman-Grobman Theorem
Dynamical Systems
2020-02-17 v1
Abstract
We showed that for any bounded neighborhood of a hyperbolic equilibrium point , there is a transformation which is locally homeomorphism, such that the system is changed into a linear system in this neighborhood. If the eigenvalues of are all located in the left-half complex plane, then there is a homeomorphism on the whole region of attraction such that the nonlinear system on the region of attraction is changed into a linear system under such a coordinate change.
Cite
@article{arxiv.2002.06094,
title = {A Global Hartman-Grobman Theorem},
author = {Xiaochang Wang},
journal= {arXiv preprint arXiv:2002.06094},
year = {2020}
}