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Article Dans Une Revue Conformal Geometry and Dynamics Année : 2011

Itération d'applications rationnelles dans les espaces de matrices

Julie Déserti

Résumé

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.

Dates et versions

hal-00604234 , version 1 (28-06-2011)

Identifiants

Citer

Dominique Cerveau, Julie Déserti. Itération d'applications rationnelles dans les espaces de matrices. Conformal Geometry and Dynamics, 2011, 15, pp.72-112. ⟨10.1090/S1088-4173-2011-00228-1⟩. ⟨hal-00604234⟩
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