English

Calculating algebraic entropies: an express method

Mathematical Physics 2017-04-26 v2 math.MP Exactly Solvable and Integrable Systems

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.

Cite

@article{arxiv.1611.05111,
  title  = {Calculating algebraic entropies: an express method},
  author = {Alfred Ramani and Basil Grammaticos and Ralph Willox and Takafumi Mase},
  journal= {arXiv preprint arXiv:1611.05111},
  year   = {2017}
}

Comments

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

R2 v1 2026-06-22T16:53:45.326Z