VOLUME PRESERVING DYNAMICS WITHOUT GENERICITY AND RELATED TOPICS
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In this article, we focus on certain dynamic phenomena in volume-preserving manifolds. Let $M$ be a compact manifold with a volume form ω and $f:M{\rightarrow}M$ be a diffeomorphism of class $\mathcal{C}^1$ that preserves ω. In this paper, we do not assume $f$ is $\mathcal{C}^1$-generic. We prove that $f$ satisfies the chain transitivity and we also show that, on $M$, the $\mathcal{C}^1$-stable shadowability is equivalent to the hyperbolicity.
Abstract
In this article, we focus on certain dynamic phenomena in volume-preserving manifolds. Let $M$ be a compact manifold with a volume form ω and $f:M{\rightarrow}M$ be a diffeomorphism of class $\mathcal{C}^1$ that preserves ω. In this paper, we do not assume $f$ is $\mathcal{C}^1$-generic. We prove that $f$ satisfies the chain transitivity and we also show that, on $M$, the $\mathcal{C}^1$-stable shadowability is equivalent to the hyperbolicity.
참고문헌 (7)
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