%0 Journal Article
%T Constraints On Dynamics Preserving Certain Hyperbolic Sets
%A Aaron W. Brown
%J Mathematics
%D 2009
%I arXiv
%R 10.1017/S014338571000009X
%X 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.
%U http://arxiv.org/abs/0906.5014v2