Discrete Painlevé equations associated with the affine Weyl group E8. (12th August 2015)

• Record Type: Journal Article
• Authors: Ramani, A; Grammaticos, B
• Is Part Of: Journal of physics. Volume 48:Number 35(2015)
• Publication Date: 2015-08-12
• Subjects: discrete Painlevé equations -- deautonomization -- integrability -- QRT mappings -- periodicity; numbers -- 02.30.Ik -- 05.45.Yv; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/35/355204
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We examine a family of discrete systems, which define analogues of the Painlevé equations, and which are related to the affine Weyl group, a domain hardly explored to date. Using the method of deautonomization we derive new integrable mappings the coefficients of which involve periodic functions with periods 14, 24 and 30. Our method is based on a novel representation of these discrete Painlevé equations, dubbed trihomographic, which we show to be generic.