Leafwise shadowing property for partially hyperbolic diffeomorphisms. Issue 2 (2nd April 2020)

• Record Type: Journal Article
• Authors: Castro, A.; Rodrigues, F.; Varandas, P.
• Is Part Of: Dynamical systems. Volume 35:Issue 2(2020)
• Page Start: 306
• Page End: 314
• Publication Date: 2020-04-02
• Subjects: Uniform and partial hyperbolicity -- leafwise shadowing property; Primary: 37C50 -- Secondary: 37D20 -- 37D30; Differentiable dynamical systems -- Periodicals; 515.35205
• DOI: 10.1080/14689367.2019.1667958
• Languages: English
• ISSNs: 1468-9367

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 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.