Differential equations which are topologically linear

Janos, Ludvik

doi:10.1090/S0002-9939-1981-0627709-7

Differential equations which are topologically linear
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by Ludvik Janos PDF

Proc. Amer. Math. Soc. 83 (1981), 629-632 Request permission

Abstract:

We show that if the flow $(R,X,\pi )$ defined by an autonomous system $\dot x = f(x)$ on a closed region $X$ of ${R^m}$ satisfies (i) it is positively nonexpansive, (ii) $X$ contains a globally asymptotically stable compact invariant subset which is a manifold, then there exists an integer $n$ so that the flow $(R,X,\pi )$ can be topologically and equivariantly embedded into the flow generated by a linear system $\dot y = Ay$ where $A$ is a constant $n \times n$ matrix.

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