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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Differential equations which are topologically linear


Author: Ludvik Janos
Journal: Proc. Amer. Math. Soc. 83 (1981), 629-632
MSC: Primary 58F10; Secondary 34C35, 54H20
DOI: https://doi.org/10.1090/S0002-9939-1981-0627709-7
MathSciNet review: 627709
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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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DOI: https://doi.org/10.1090/S0002-9939-1981-0627709-7
Article copyright: © Copyright 1981 American Mathematical Society