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Singularity, complexity, and quasi-integrability of rational mappings

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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 propertiesqua dynamical systems, making contact with Arnol'd's notion of complexity, and exemplify remarkable behaviours.

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Authors and Affiliations

  1. Laboratoire de Physique Théorique et des Hautes Energies, Unité Associée au CNRS (URA 280), Université Paris VI Boîte 126, Tour 16-1er Etage/4 Place Jussieu, F-75252, Paris Cedex 05, France

    G. Falqui & C. -M. Viallet

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  1. G. Falqui
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  2. C. -M. Viallet
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Communicated by K. Gawedzki

Supported in part by Ministère de la Recherche et de la Technologie

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Falqui, G., Viallet, C.M. Singularity, complexity, and quasi-integrability of rational mappings. Commun.Math. Phys. 154, 111–125 (1993). https://doi.org/10.1007/BF02096835

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