TY - JOUR
T1 - Constraints on dynamics preserving certain hyperbolic sets
AU - Brown, Aaron W
PY - 2011/6
Y1 - 2011/6
N2 - We establish two results under which the topology of a compact hyperbolic set constrains ambient dynamics. First, if Λ is a transitive, codimension-one, expanding attractor for some diffeomorphism, then Λ is a union of transitive, codimension-one attractors (or contracting repellers) for any diffeomorphism such that Λ is hyperbolic. Secondly, if Λ is a locally maximal nonwandering set for a surface diffeomorphism, then Λ is locally maximal for any diffeomorphism for which Λ is hyperbolic.
AB - We establish two results under which the topology of a compact hyperbolic set constrains ambient dynamics. First, if Λ is a transitive, codimension-one, expanding attractor for some diffeomorphism, then Λ is a union of transitive, codimension-one attractors (or contracting repellers) for any diffeomorphism such that Λ is hyperbolic. Secondly, if Λ is a locally maximal nonwandering set for a surface diffeomorphism, then Λ is locally maximal for any diffeomorphism for which Λ is hyperbolic.
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U2 - 10.1017/S014338571000009X
DO - 10.1017/S014338571000009X
M3 - Article
AN - SCOPUS:79956068214
SN - 0143-3857
VL - 31
SP - 719
EP - 739
JO - Ergodic Theory and Dynamical Systems
JF - Ergodic Theory and Dynamical Systems
IS - 3
ER -