Attractors of direct products

Stanislav Minkov, Ivan Shilin

Published 2020-11-09Version 1

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 an SRB-measure such that its square does not coincide with an SRB-measure of the square of $\varphi$.