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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Stability and skew-product flows


Author: Jirō Egawa
Journal: Proc. Amer. Math. Soc. 101 (1987), 484-486
MSC: Primary 54H20; Secondary 34A10, 34D20
MathSciNet review: 908653
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Abstract: We consider a skew-product flow with a minimal flow as the basic flow, and we show that, if a bounded solution is positively uniformly stable, then the $ \omega $-limit set of it is a minimal set. This is an extension of a result in [2], where it was assumed that the basic flow is equicontinuous.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1987-0908653-X
PII: S 0002-9939(1987)0908653-X
Keywords: Skew-product flow, uniformly stable, minimal set, minimal flow, $ \omega $-limit set, of distal type, homomorphism
Article copyright: © Copyright 1987 American Mathematical Society