Integrable mappings and the notion of anticonfinement. (1st June 2018)

• Record Type: Journal Article
• Authors: Mase, T; Willox, R; Ramani, A; Grammaticos, B
• Is Part Of: Journal of physics. Volume 51:Number 26(2018)
• Publication Date: 2018-06-01
• Subjects: mapping -- integrability -- deautonomisation -- singularity -- degree growth; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8121/aac578
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: We examine the notion of anticonfinement and the role it has to play in the singularity analysis of discrete systems. A singularity is said to be anticonfined if singular values continue to arise indefinitely for the forward and backward iterations of a mapping, with only a finite number of iterates taking regular values in between. We show through several concrete examples that the behaviour of some anticonfined singularities is strongly related to the integrability properties of the discrete mappings in which they arise, and we explain how to use this information to decide on the integrability or non-integrability of the mapping.