On Homoclinic points, Recurrences and Chain recurrences of volume-preserving diffeomorphisms without genericity

Jaeyoo Choy, Hahng-Yun Chu, Min Kyu Kim

Let $M$ be a manifold with a volume form $\omega$ and $f:M\to M$ be a diffeomorphism of class ${\mathcal{C}}^1$ that preserves $\omega$. In this paper, we do \textit{not} assume $f$ is $\ma…