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Bull. Korean Math. Soc. 2014; 51(5): 1259-1267
Printed September 30, 2014
https://doi.org/10.4134/BKMS.2014.51.5.1259
Copyright © The Korean Mathematical Society.
Hyperbolicity of chain transitive sets with limit shadowing
Abbas Fakhari, Seunghee Lee, and Khosro Tajbakhsh
Shahid Beheshti University, Chungnam National University, Tarbiat Modares University
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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