  For Milnor, statistical, and minimal attractors, we construct examples of
smooth flows $\varphi$ on $S^2$ for which the attractor of the Cartesian square
of $\varphi$ is smaller than the Cartesian square of the attractor of
$\varphi$. In the example for the minimal attractors, the flow $\varphi$ also
has a global physical measure such that its square does not coincide with the
global physical measure of the square of $\varphi$.
