Calculating algebraic entropies: an express method. (6th April 2017)

• Record Type: Journal Article
• Authors: Ramani, A; Grammaticos, B; Willox, R; Mase, T
• Is Part Of: Journal of physics. Volume 50:Number 18(2017)
• Publication Date: 2017-04-06
• Subjects: mappings -- integrability -- deautonomisation -- singularities -- algebraic entropy; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aa66d7
• Languages: English
• ISSNs: 1751-8113

Abstract

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 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.