Constraints On Dynamics Preserving Certain Hyperbolic Sets

Details Constraints On Dynamics Preserving Certain Hyperbolic Sets Constraints On Dynamics Preserving Certain Hyperbolic Sets

2009-06-26

arxiv.org/abs/0906.5014v2

Mathematics

Dynamical Systems

19 pages

Scientific paper

10.1017/S014338571000009X

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

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