Geodesic
Local maximality of hyperbolic sets
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, Tome 273 (2011), pp. 28-29

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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 $F$. 
@article{TM_2011_273_a1,
     author = {D. V. Anosov},
     title = {Local maximality of hyperbolic sets},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {28--29},
     publisher = {mathdoc},
     volume = {273},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2011_273_a1/}
}
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D. V. Anosov. Local maximality of hyperbolic sets. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Modern problems of mathematics, Tome 273 (2011), pp. 28-29. http://geodesic.mathdoc.fr/item/TM_2011_273_a1/