Communications in Information and Systems

Volume 22 (2022)

Number 1

A global Hartman–Grobman theorem

Pages: 39 – 52

DOI: https://dx.doi.org/10.4310/CIS.2022.v22.n1.a2

Authors

Xiaochang Wang (Department of Mathematics and Statistics, Texas Tech University, Lubbock, Tx., U.S.A.)

Jiexin Dai (Department of Mathematics and Statistics, Texas Tech University, Lubbock, Tx., U.S.A.)

Abstract

We showed that for any bounded neighborhood of a hyperbolic equilibrium point $x_0$, 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 $Df(x_0)$ 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.

Keywords

Hartman–Grobman theorem

2010 Mathematics Subject Classification

34A34

The full text of this article is unavailable through your IP address: 100.28.132.102

Received 1 September 2020

Published 7 February 2022