• Title/Summary/Keyword: Kronecker foliation

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A TOPOLOGICAL MIRROR SYMMETRY ON NONCOMMUTATIVE COMPLEX TWO-TORI

  • Kim, Eun-Sang;Kim, Ho-Il
    • Journal of the Korean Mathematical Society
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    • v.43 no.5
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    • pp.951-965
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    • 2006
  • In this paper, we study a topological mirror symmetry on noncommutative complex tori. We show that deformation quantization of an elliptic curve is mirror symmetric to an irrational rotation algebra. From this, we conclude that a mirror reflection of a noncommutative complex torus is an elliptic curve equipped with a Kronecker foliation.

HYPERBOLICITY OF CHAIN TRANSITIVE SETS WITH LIMIT SHADOWING

  • Fakhari, Abbas;Lee, Seunghee;Tajbakhsh, Khosro
    • Bulletin of the Korean Mathematical Society
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    • v.51 no.5
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    • pp.1259-1267
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    • 2014
  • 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.