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Acta Mathematica Sinica, English Series

, Volume 30, Issue 6, pp 1007–1020 | Cite as

Stable weakly shadowable volume-preserving systems are volume-hyperbolic

  • Mário Bessa
  • Manseob Lee
  • Sandra Vaz
Article

Abstract

We prove that any C 1-stable weakly shadowable volume-preserving diffeomorphism de-fined on a compact manifold displays a dominated splitting EF. Moreover, both E and F are volume-hyperbolic. Finally, we prove the version of this result for divergence-free vector fields. As a consequence, in low dimensions, we obtain global hyperbolicity.

Keywords

Weak shadowing dominated splitting hyperbolicity 

MR(2010) Subject Classification

37C50 37D30 37C10 

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Copyright information

© Institute of Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Chinese Mathematical Society and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.Rua Marquês d’Ávila e BolamaUniversidade da Beira InteriorCovilhãPortugal
  2. 2.Department of MathematicsMokwon UniversityDaejeonRepublic of Korea

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