Itération d’applications rationnelles dans les espaces de matrices

Cerveau, Dominique; Déserti, Julie

doi:10.1090/S1088-4173-2011-00228-1

Itération d’applications rationnelles dans les espaces de matrices
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by Dominique Cerveau and Julie Déserti

Conform. Geom. Dyn. 15 (2011), 72-112

DOI: https://doi.org/10.1090/S1088-4173-2011-00228-1

Published electronically: August 1, 2011

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Abstract:

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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