Itération d'applications rationnelles dans les espaces de matrices

Details Itération d'applications rationnelles dans les espaces de matrices Itération d'applications rationnelles dans les espaces de matrices

2011-02-23

arxiv.org/abs/1102.4738v2

Mathematics

Dynamical Systems

accepted in Conform. Geom. Dyn

Scientific paper

The iteration of rational maps is well-understood in dimension 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 $\mathrm{M}$ onto $\mathrm{M}^2$ for which we exhibit some dynamical properties. Finally we deal with some small perturbations of this map.

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