Kyungpook Mathematical Journal

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Chain Recurrences on Conservative Dynamics

  • Choy, Jaeyoo (Department of Mathematics, Kyungpook National University) ;
  • Chu, Hahng-Yun (Department of Mathematics, Chungnam National University)
  • Received : 2014.01.27
  • Accepted : 2014.05.22
  • Published : 2014.06.23
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Abstract

Let M be a manifold with a volume form ${\omega}$ and $f:M{\rightarrow}M$ be a diffeomorphism of class π’ž$^1$ that preserves ${\omega}$. We prove that if M is almost bounded for the diffeomorphism f, then M is chain recurrent. Moreover, we get that Lagrange stable volume-preserving manifolds are also chain recurrent.

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References

  1. M. Arnaud, C. Bonatti and S. Crovisier, Dynamiques symplectiques generiques, Er-godic Theory Dynam. Systems, 25(2005), 1401-1436. https://doi.org/10.1017/S0143385704000975
  2. J. Choy and H.-Y. Chu, On the Envelopes of Homotopies, Kyungpook Math. J., 49(3)(2009), 573-582. https://doi.org/10.5666/KMJ.2009.49.3.573
  3. J. Choy, H.-Y. Chu and M. Kim, Volume preserving dynamics without genericity and related topics, Commun. Korean Math. Soc., 27(2012), 369-375. https://doi.org/10.4134/CKMS.2012.27.2.369
  4. C. Conley, Isolated invariant sets and the morse index, C. B. M. S. Regional Lect., 38(1978).
  5. M. Hurley, Chain recurrence and attraction in noncompact spaces, Ergodic Theory Dynam. Systems, 11(1991), 709-729.
  6. M. Hurley, Noncompact chain recurrence and attraction, Proc. Amer. Math. Soc., 115(1992), 1139-1148. https://doi.org/10.1090/S0002-9939-1992-1098401-X