On the canonical forms of QRT mappings and discrete Painlevé equations. (3rd September 2018)

• Record Type: Journal Article
• Authors: Ramani, A; Grammaticos, B; Satsuma, J; Tamizhmani, T
• Is Part Of: Journal of physics. Volume 51:Number 39(2018)
• Publication Date: 2018-09-03
• Subjects: mappings -- integrability -- deautonomisation -- singularities -- discrete Painlevé equations -- canonical forms; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aad8c3
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We derive systematically the canonical forms of the Quispel–Roberts–Thompson (QRT) mappings and obtain two new forms which were absent in the previous classifications. They correspond to what, in QRT parlance are called, asymmetric mappings. We derive the generic discrete Painlevé equations associated with these canonical forms, as well as some non-generic ones. We study the singularity structure of one of the latter and show that it possesses anticonfined singularities, a new phenomenon for discrete Painlevé equations.