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On asymptotically stable sets

Published online by Cambridge University Press:  20 January 2009

D. Desbrow
D. Desbrow
Affiliation:
University of Edinburgh, Edinburgh EH1 1HZ
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In this paper we study closed sets having a neighbourhood with compact closure which are positively asymptotically stable under a flow on a metric space X. For an understanding of this and the rest of the introduction it is sufficient for the reader to have in mind as an example of a flow a system of first order, autonomous ordinary differential equations describing mathematically a time-independent physical system; in short a dynamical system. In a flow a set M is positively stable if the trajectories through all points sufficiently close to M remain in the future in a given neighbourhood of M. The set M is positively asymptotically stable if it is positively stable and, in addition, trajectories through all points of some neighbourhood of M approach M in the future.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 17 , Issue 2 , December 1970 , pp. 181 - 186
Copyright
Copyright © Edinburgh Mathematical Society 1970

References

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