Geodesic
Classification of compact invariant sets of dynamical systems
Izvestiya. Mathematics , Tome 43 (1994) no. 3, pp. 517-526.

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A classification of the compact invariant sets of a dynamical system in a locally compact complete metric space is given with respect to the properties of stability, attraction, isolation, and others. 
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A. F. Filippov. Classification of compact invariant sets of dynamical systems. Izvestiya. Mathematics , Tome 43 (1994) no. 3, pp. 517-526. http://geodesic.mathdoc.fr/item/IM2_1994_43_3_a6/

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