Leafwise shadowing property for partially hyperbolic diffeomorphisms. Issue 2 (2nd April 2020) - Castro, A.; Rodrigues, F.; Varandas, P.
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 C 1 -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 C 1 -close diffeomorphisms. Similar results hold for open classes of strongly partially hyperbolic diffeomorphisms.