Communications in Information and Systems
Volume 22 (2022)
A global Hartman–Grobman theorem
Pages: 39 – 52
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.
2010 Mathematics Subject Classification
Received 1 September 2020
Published 7 February 2022