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Chain Recurrences on Conservative Dynamics

Choy, Jaeyoo;Chu, Hahng-Yun

  • Received : 2014.01.27
  • Accepted : 2014.05.22
  • Published : 2014.06.23

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.

Keywords

volume-preserving;chain recurrence;almost unbounded;Lagrange-stable;attractors

References

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Acknowledgement

Supported by : National Research Foundation of Korea(NRF)