Local maximality of hyperbolic sets

Local maximality of hyperbolic sets

Two properties of a hyperbolic set F are discussed: its local maximality and the property that, in any neighborhood U ⊃ 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...

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Bibliographic Details
Published in:Proceedings of the Steklov Institute of Mathematics Vol. 273; no. 1; pp. 23 - 24
Main Author: Anosov, D. V.
Format: Journal Article
Language:English
Published: Dordrecht SP MAIK Nauka/Interperiodica 01-07-2011
Subjects:
Mathematics
Mathematics and Statistics
Intrinsic Property
STEKLOV Institute
75th Anniversary
Smooth Manifold
Local Maximality
Online Access:Get full text
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Summary:Two properties of a hyperbolic set F are discussed: its local maximality and the property that, in any neighborhood U ⊃ 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 .
ISSN:0081-5438
1531-8605
DOI:10.1134/S008154381104002X