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Conformal Geometry and Dynamics

ISSN 1088-4173



Itération d’applications rationnelles dans les espaces de matrices

Authors: Dominique Cerveau and Julie Déserti
Journal: Conform. Geom. Dyn. 15 (2011), 72-112
MSC (2010): Primary 14E05, 32H50, 37B05
Published electronically: August 1, 2011
MathSciNet review: 2833474
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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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Additional Information

Dominique Cerveau
Affiliation: Membre de l’Institut Universitaire de France. IRMAR, UMR 6625 du CNRS, Université de Rennes 1, 35042 Rennes, France

Julie Déserti
Affiliation: Institut de Mathématiques de Jussieu, Université Paris 7, Projet Géométrie et Dynamique, Site Chevaleret, Case 7012, 75205 Paris Cedex 13, France
Address at time of publication: Universität Basel, Mathematisches Institut, Rheinsprung 21, CH-4051, Basel, Switzerland

Received by editor(s): March 7, 2011
Published electronically: August 1, 2011
Article copyright: © Copyright 2011 American Mathematical Society