Geodesic
Local maximality of hyperbolic sets
Informatics and Automation, Modern problems of mathematics, Tome 273 (2011), pp. 28-29 
D. V. Anosov. Local maximality of hyperbolic sets. Informatics and Automation, Modern problems of mathematics, Tome 273 (2011), pp. 28-29. http://geodesic.mathdoc.fr/item/TRSPY_2011_273_a1/
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     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TRSPY_2011_273_a1/}
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Voir la notice de l'article provenant de la source Math-Net.Ru

Two properties of a hyperbolic set $F$ are discussed: its local maximality and the property that, in any neighborhood $U\supset F$, there exists a locally maximal set $F'$ that contains $F$ (we suggest calling the latter property local premaximality). Although both these properties of the set $F$ are related to the behavior of trajectories outside $F$, it turns out that, in the class of hyperbolic sets, the presence or absence of these properties is determined by the interior dynamics on $F$.

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