On the existence of attractors

Christian Bonatti, Ming Li, Dawei Yang

On every compact 3-manifold, we build a non-empty open set $\cU$ of $\Diff^1(M)$ such that, for every $r\ge 1$, every $C^r$-generic diffeomorphism $f\in\cU\cap \Diff^r(M)$ has no…