[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.5666/KMJ.2014.54.2.165

Chain Recurrences on Conservative Dynamics

Choy, Jaeyoo (Department of Mathematics, Kyungpook National University)
Chu, Hahng-Yun (Department of Mathematics, Chungnam National University)

Publication Information

Kyungpook Mathematical Journal / v.54, no.2, 2014 , pp. 165-171 More about this Journal

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;

Citations & Related Records

Times Cited By KSCI : 2 (Citation Analysis)

Reference
Cited By KSCI

1	M. Arnaud, C. Bonatti and S. Crovisier, Dynamiques symplectiques generiques, Er-godic Theory Dynam. Systems, 25(2005), 1401-1436. DOI ScienceOn
2	J. Choy and H.-Y. Chu, On the Envelopes of Homotopies, Kyungpook Math. J., 49(3)(2009), 573-582. 과학기술학회마을 DOI ScienceOn
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. 과학기술학회마을 DOI ScienceOn
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. DOI