My question is in the title. You can imagine 1D or 2D maps for example, the simpler the better. Let us say we have chaotic map T and chaotic map R. We need that RT(x(n))=TR(x(n)). (I do not want R= invertible map and $T=R^{-1}$ or $T=R \circ R$).
(Motivation for this question is probably stupid. I imagine series in time and in space (just x direction), which is chaotic in both of this directions. In t - direction operates T and and in x - direction operates R. To have x, t structure one needs commutation of these maps. Though, I hope the question have its relevance in itself.)