Attractors of direct products

Abstract

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

31 pages, 2 figures