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Constraints on dynamics preserving certain hyperbolic sets

Published online by Cambridge University Press:  26 May 2010

AARON W. BROWN
AARON W. BROWN*
Affiliation:
Tufts University, Medford, MA 02155, USA (email: [email protected])
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Abstract

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.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 31 , Issue 3 , June 2011 , pp. 719 - 739
Copyright
Copyright © Cambridge University Press 2010

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