The redemption of singularity confinement. (25th February 2015)

• Record Type: Journal Article
• Authors: Ramani, A; Grammaticos, B; Willox, R; Mase, T; Kanki, M
• Is Part Of: Journal of physics. Volume 48:Number 11(2015)
• Publication Date: 2015-02-25
• Subjects: mappings -- integrability -- signularities -- deautonomization; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/11/11FT02
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We present a novel way to apply the singularity confinement property as a discrete integrability criterion. We shall use what we call a full deautonomization approach, which consists in treating the free parameters in the mapping as functions of the independent variable, applied to a mapping complemented with terms that are absent in the original mapping but which do not change the singularity structure. We shall show, on a host of examples including the well-known mapping of Hietarinta–Viallet, that our approach offers a way to compute the algebraic entropy for these mappings exactly, thereby allowing one to distinguish between the integrable and non-integrable cases even when both have confined singularities.