Abstract
ABSTRACT In this note, we characterize hyperbolicity of invariant laminations for partially hyperbolic diffeomorphisms in terms of a leafwise shadowing property. We prove that a -diffeomorphism with partially hyperbolic non-wandering set is Axiom A if and only if the leafwise shadowing property holds along the central lamination for all -close diffeomorphisms. Similar results hold for open classes of strongly partially hyperbolic diffeomorphisms.
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