Abstract
The iteration of rational maps is well understood in dimension 1 1 but less so in higher dimensions. We study some maps on spaces of matrices which present a weak complexity with respect to the ring structure. First, we give some properties of certain rational maps; the simplest example is the rational map which sends the matrix M \mathrm {M} onto M 2 \mathrm {M}^2 for which we exhibit some dynamical properties. Finally, we deal with some small perturbations of this map.
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