2016/03/01 by Ralph Willox, Takafumi Mase, Alfred Ramani +3 · 1 citation
Mathematics · Physics and Astronomy · #Condensed matter physics #Lattice (music) #Mathematical physics #Mathematics #Nonlinear Waves and Solitons #Physics #Quantum chaos and dynamical systems #Statistical physics #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.1088/1751-8113/49/28/28lt01
11 pages, 2 figures
arxiv created 2016/03/01 · openalex publication_date 2016/05/31 · arxiv updated 2016/06/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
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.