VOLUME PRESERVING DYNAMICS WITHOUT GENERICITY AND RELATED TOPICS

Title & Authors
VOLUME PRESERVING DYNAMICS WITHOUT GENERICITY AND RELATED TOPICS
Choy, Jae-Yoo; Chu, Hahng-Yun; Kim, Min-Kyu;

Abstract
In this article, we focus on certain dynamic phenomena in volume-preserving manifolds. Let $\small{M}$ be a compact manifold with a volume form $\small{{\omega}}$ and $\small{f:M{\rightarrow}M}$ be a diffeomorphism of class $\small{\mathcal{C}^1}$ that preserves $\small{{\omega}}$. In this paper, we do not assume $\small{f}$ is $\small{\mathcal{C}^1}$-generic. We prove that $\small{f}$ satisfies the chain transitivity and we also show that, on $\small{M}$, the $\small{\mathcal{C}^1}$-stable shadowability is equivalent to the hyperbolicity.
Keywords
hyperbolicity;$\small{\mathcal{C}^1}$-stable shadowable;chain recurrence;chain transitive;
Language
English
Cited by
1.
Chain Recurrences on Conservative Dynamics,;;

Kyungpook mathematical journal, 2014. vol.54. 2, pp.165-171
1.
Chain Recurrences on Conservative Dynamics, Kyungpook mathematical journal, 2014, 54, 2, 165
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