Attractors of direct products

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 \(\varphi\).