Stable, asymptotically stable

The following definition is a translation to this setting of the classical definition as found in the book by LaSalle and Lefschetz [9].

Definition: A compact invariant set Stable1.jpg is called stable if for each neighborhood Stable2.jpg of Stable3.jpg there exists a neighborhood Stable4.jpg of Stable5.jpg such that

Stable6.jpg

The set is called asymptotically stable if it is stable and if there exists a neighborhood Stable7.jpg of Stable8.jpg such that Stable9.jpg .


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Copyright (c) 1998 by Richard McGehee, all rights reserved.
Last modified: July 31, 1998.