Full-deautonomisation of a lattice equation. (31st May 2016)

• Record Type: Journal Article
• Authors: Willox, R; Mase, T; Ramani, A; Grammaticos, B
• Is Part Of: Journal of physics. Volume 49:Number 28(2016)
• Publication Date: 2016-05-31
• Subjects: lattice equation -- integrability -- deautonomisation -- singularity -- degree growth; 02.30.Ik -- 05.45.Yv; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/49/28/28LT01
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: In this letter we report on the unexpected possibility of applying the full-deautonomisation approach we recently proposed for predicting the algebraic entropy of second-order birational mappings, to discrete lattice equations. Moreover, we show, on two examples, that the full-deautonomisation technique can in fact also be successfully applied to reductions of these lattice equations to mappings with orders higher than 2. In particular, we apply this technique to a recently discovered lattice equation that has confined singularities while being nonintegrable, and we show that our approach accurately predicts this nonintegrable character. Finally, we demonstrate how our method can even be used to predict the algebraic entropy for some nonconfining higher order mappings.