2018/03/31 by Ryo Kamiya, Masataka Kanki, Takafumi Mase +2
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Class (philosophy) #Computer science #Gravitational singularity #Integer (computer science) #Integrable system #Iterated function #Lattice (music) #Mathematical analysis #Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Physics #Pure mathematics #Singularity #Toda lattice #math-ph #math.AC #math.MP #msc:13F60 #msc:37K10 #nlin.SI
paper · pdf · doi:10.1088/1751-8121/aad375
published as J. Phys. A: Math. Theor. 51 (2018) 364002 (16pp) · 13 pages
arxiv created 2018/05/23 · openalex publication_date 2018/07/13 · arxiv updated 2018/08/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
Abstract We introduce a class of recursions defined over the d -dimensional integer lattice. The discrete equations we study are interpreted as higher dimensional extensions to the discrete Toda lattice equation. We shall prove that the equations satisfy the coprimeness property, which is one of integrability detectors analogous to the singularity confinement test. While the degree of their iterates grows exponentially, their singularities exhibit a nature similar to that of integrable systems in terms of the coprimeness property. We also prove that the equations can be expressed as mutations of a seed in the sense of the Laurent phenomenon algebra.