It\'eration d'applications rationnelles dans les espaces de matrices
D. Cerveau, J. D\'eserti

TL;DR
This paper investigates the dynamics of rational maps on matrix spaces, focusing on maps like squaring matrices and their perturbations, extending understanding from one-dimensional cases to higher dimensions.
Contribution
It introduces new properties of rational maps on matrix spaces and analyzes their dynamical behavior, including perturbations, in higher-dimensional settings.
Findings
Analysis of the map M -> M^2 and its dynamical properties
Characterization of weak complexity in matrix rational maps
Behavior of small perturbations of the squaring map
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 onto for which we exhibit some dynamical properties. Finally we deal with some small perturbations of this map.
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Taxonomy
TopicsAdvanced Differential Equations and Dynamical Systems · Advanced Topics in Algebra · Mathematical Dynamics and Fractals
