Robustly shadowable chain transtive sets and hyperbolicity

2017/03/06 by Bagherzad, Mohammad Reza, Lee, Keonhee
#Dynamical Systems (math.DS) #FOS: Mathematics

paper · doi:10.48550/arxiv.1703.02010

Abstract

We say that a compact invariant set Λ of a C¹-vector field X on a compact boundaryless Riemannian manifold M is robustly shadowable if it is locally maximal with respect to a neighborhood U of Λ, and there exists a C¹-neigborhood U of X such that for any Y ∈ U, the continuation Λ_Y of Λ for Y and U is shadowable for Y_t. In this paper, we prove that any chain transitive set of a C¹-vector field on M is hyperbolic if and only if it is robustly shadowable.

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