@inbook{28e80dab1d7b4c00bc9da39c9cda75fe,

title = "Chain transitive sets and shadowing",

abstract = "In this chapter, we study relations between the shadowing property of diffeomorphisms on their chain transitive sets and the hyperbolicity of such sets. We prove the following two main results: • Let ⋀ be a closed invariant set of f ϵ Diff1(M). Then f|⋀ is chain transitive and C1-stably shadowing in a neighborhood of ⋀ if and only if ⋀ is a hyperbolic basic set (Theorem 4.2.1); • there is a residual set R ⊂ Diff1(M) such that if f ϵ R and ⋀ is a locally maximal chain transitive set of f, then ⋀ is hyperbolic if and only if f |⋀ is shadowing (Theorem 4.3.1).",

author = "Pilyugin, {Sergei Yu} and Kazuhiro Sakai",

note = "Publisher Copyright: {\textcopyright} Springer International Publishing AG 2017. Copyright: Copyright 2017 Elsevier B.V., All rights reserved.",

year = "2017",

doi = "10.1007/978-3-319-65184-2_4",

language = "English",

series = "Lecture Notes in Mathematics",

publisher = "Springer Nature",

pages = "181--208",

booktitle = "Lecture Notes in Mathematics",

address = "Germany",

}