Singularity, complexity, and quasi--integrability of rational mappings
High Energy Physics - Theory
2009-10-22 v1 alg-geom
Algebraic Geometry
Abstract
We investigate global properties of the mappings entering the description of symmetries of integrable spin and vertex models, by exploiting their nature of birational transformations of projective spaces. We give an algorithmic analysis of the structure of invariants of such mappings. We discuss some characteristic conditions for their (quasi)--integrability, and in particular its links with their singularities (in the 2--plane). Finally, we describe some of their properties {\it qua\/} dynamical systems, making contact with Arnol'd's notion of complexity, and exemplify remarkable behaviours.
Cite
@article{arxiv.hep-th/9212105,
title = {Singularity, complexity, and quasi--integrability of rational mappings},
author = {G. Falqui and C. -M. Viallet},
journal= {arXiv preprint arXiv:hep-th/9212105},
year = {2009}
}
Comments
Latex file. 17 pages. To appear in CMP