# Chain Recurrences on Conservative Dynamics

Choy, Jaeyoo;Chu, Hahng-Yun

• Accepted : 2014.05.22
• Published : 2014.06.23
• 21 7

#### Abstract

Let M be a manifold with a volume form ${\omega}$ and $f:M{\rightarrow}M$ be a diffeomorphism of class 𝒞$^1$ 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)