VOLUME PRESERVING DYNAMICS WITHOUT GENERICITY AND RELATED TOPICS Choy, Jae-Yoo; Chu, Hahng-Yun; Kim, Min-Kyu;
In this article, we focus on certain dynamic phenomena in volume-preserving manifolds. Let be a compact manifold with a volume form and be a diffeomorphism of class that preserves . In this paper, we do not assume is -generic. We prove that satisfies the chain transitivity and we also show that, on , the -stable shadowability is equivalent to the hyperbolicity.