Hyperbolicity of chain transitive sets with limit shadowing
Bull. Korean Math. Soc. 2014 Vol. 51, No. 5, 1259-1267
https://doi.org/10.4134/BKMS.2014.51.5.1259
Printed September 30, 2014
Abbas Fakhari, Seunghee Lee, and Khosro Tajbakhsh
Shahid Beheshti University, Chungnam National University, Tarbiat Modares University
Abstract : In this paper we show that any chain transitive set of a diffeomorphism on a compact $C^{\infty}$-manifold which is $C^1$-stably limit shadowable is hyperbolic. Moreover, it is proved that a locally maximal chain transitive set of a $C^1$-generic diffeomorphism is hyperbolic if and only if it is limit shadowable.
Keywords : noncommutative complex torus, mirror symmetry, Kronecker foliation
MSC numbers : Primary 58B34, 58J42, 81T75
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