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