Abstract
The paper is devoted to the local premaximality property in the class of hyperbolic sets. (An invariant set F of a diffeomorphism S has this property, if it is not locally maximal, but in any neighborhood of F there exists a locally maximal invariant set containing F.) We prove that (in this class) the property of F to be or not to be locally premaximal depends only on the “interior dynamics” inside F, i.e. it depends only on the restriction S|F.
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Supported by the Program of the Presidium of Russian Academy of Sciences “Mathematical Control Theory” and by the grant of Russian Foundation for Basic Research No. 08-01-00342.
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Anosov, D.V. Intrinsic Character of One Property of Hyperbolic Sets. J Dyn Control Syst 16, 485–493 (2010). https://doi.org/10.1007/s10883-010-9103-y
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DOI: https://doi.org/10.1007/s10883-010-9103-y