Singularity, complexity, and quasi--integrability of rational mappings

Details Singularity, complexity, and quasi--integrability of rational mappings Singularity, complexity, and quasi--integrability of rational mappings

1992-12-17

arxiv.org/abs/hep-th/9212105v1

Commun.Math.Phys. 154 (1993) 111-126

Physics

High Energy Physics

High Energy Physics - Theory

Latex file. 17 pages. To appear in CMP

Scientific paper

10.1007/BF02096835

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.

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