Geodesic
Density of the set of attractive compacta
Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part V, Tome 143 (1985), pp. 170-175 Cet article a éte moissonné depuis la source Math-Net.Ru

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A compact set $K$ in a smooth closed manifold $M$ is said to be attractive, if on $M$ there exists a system of differential equations, for which $K$ is an asymptotically stable invariant set. It is proved that the set of attractive compacta is dense and its complement contains a dense set of type $G_\delta$ in the space of all compacta of the manifold $M$ endowed with two natural topologies. 
@article{ZNSL_1985_143_a10,
     author = {S. Yu. Pilyugin},
     title = {Density of the set of attractive compacta},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {170--175},
     year = {1985},
     volume = {143},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1985_143_a10/}
}
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S. Yu. Pilyugin. Density of the set of attractive compacta. Zapiski Nauchnykh Seminarov POMI, Investigations in topology. Part V, Tome 143 (1985), pp. 170-175. http://geodesic.mathdoc.fr/item/ZNSL_1985_143_a10/