  On every compact 3-manifold, we build a non-empty open set $\cU$ of
$\Diff^1(M)$ such that, for every $r\geq 1$, every $C^r$-generic diffeomorphism
$f\in\cU\cap \Diff^r(M)$ has no topological attractors. On higher dimensional
manifolds, one may require that $f$ has neither topological attractors nor
topological repellers. Our examples have finitely many quasi attractors. For
flows, we may require that these quasi attractors contain singular points.
Finally we discuss alternative definitions of attractors which may be better
adapted to generic dynamics.
