Calculating algebraic entropies: an express method

Abstract

We describe a method for investigating the integrable character of a given three-point mapping, provided that the mapping has confined singularities. Our method, dubbed "express", is inspired by a novel approach recently proposed by R.G. Halburd. While the latter aims at computing the exact degree growth of a given mapping based on the structure of its singularities, we content ourselves with obtaining an answer as to whether a given system is integrable or not. We present several examples illustrating our method as well as its limitations. We also compare the present method to the full-deautonomisation approach we recently introduced.

11 pages, no figures ; eq. (21) corrected

References in corpus (2)

• Deautonomisation by singularity confinement: an algebro-geometric justification
• Singularity confinement and full-deautonomisation: a discrete integrability criterion

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