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arXiv · 2002.06094

A Global Hartman-Grobman Theorem

Xiaochang Wang
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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.

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Xiaochang Wang. 2020-02-14. A Global Hartman-Grobman Theorem. https://arxiv.org/abs/2002.06094

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