On the complexity of some birational transformations
Mathematical Physics
2011-11-10 v1 math.MP
Chaotic Dynamics
Abstract
Using three different approaches, we analyze the complexity of various birational maps constructed from simple operations (inversions) on square matrices of arbitrary size. The first approach consists in the study of the images of lines, and relies mainly on univariate polynomial algebra, the second approach is a singularity analysis, and the third method is more numerical, using integer arithmetics. Each method has its own domain of application, but they give corroborating results, and lead us to a conjecture on the complexity of a class of maps constructed from matrix inversions.
Cite
@article{arxiv.math-ph/0503074,
title = {On the complexity of some birational transformations},
author = {Jean Christian Angles D'Auriac and Jean-Marie Maillard and Claude Viallet},
journal= {arXiv preprint arXiv:math-ph/0503074},
year = {2011}
}