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Conformal Geometry and Dynamics

Published by the American Mathematical Society, the Conformal Geometry and Dynamics (ECGD) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-4173

The 2020 MCQ for Conformal Geometry and Dynamics is 0.5.

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Itération d’applications rationnelles dans les espaces de matrices
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by Dominique Cerveau and Julie Déserti PDF
Conform. Geom. Dyn. 15 (2011), 72-112 Request permission

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
  • Email: dominique.cerveau@univ-rennes1.fr
  • 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
  • Email: deserti@math.jussieu.fr
  • Received by editor(s): March 7, 2011
  • Published electronically: August 1, 2011
  • © Copyright 2011 American Mathematical Society
  • Journal: Conform. Geom. Dyn. 15 (2011), 72-112
  • MSC (2010): Primary 14E05, 32H50, 37B05
  • DOI: https://doi.org/10.1090/S1088-4173-2011-00228-1
  • MathSciNet review: 2833474