Constraints On Dynamics Preserving Certain Hyperbolic Sets
نویسنده
چکیده
We establish two results under which the topology of a hyperbolic set constrains ambient dynamics. First if Λ is a compact, transitive, expanding hyperbolic attractor of codimension 1 for some diffeomorphism, then Λ is a union of transitive, expanding attractors (or contracting repellers) of codimension 1 for any diffeomorphism such that Λ is hyperbolic. Secondly, if Λ is a nonwandering, locally maximal, compact hyperbolic set for a surface diffeomorphism, then Λ is locally maximal for any diffeomorphism for which Λ is hyperbolic.
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