Stability and skew-product flows
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- by Jirō Egawa PDF
- Proc. Amer. Math. Soc. 101 (1987), 484-486 Request permission
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.References
- B. M. Levitan and V. V. Zhikov, Almost periodic functions and differential equations, Cambridge University Press, Cambridge-New York, 1982. Translated from the Russian by L. W. Longdon. MR 690064
- Robert J. Sacker and George R. Sell, Lifting properties in skew-product flows with applications to differential equations, Mem. Amer. Math. Soc. 11 (1977), no. 190, iv+67. MR 448325, DOI 10.1090/memo/0190
Additional Information
- © Copyright 1987 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 101 (1987), 484-486
- MSC: Primary 54H20; Secondary 34A10, 34D20
- DOI: https://doi.org/10.1090/S0002-9939-1987-0908653-X
- MathSciNet review: 908653