263 citations · 921 across the 24 of their papers we have counts for
9 papers · 1 filter
Algebraic entropy for hex systems
Giorgio Gubbiotti, Andrew P. Kels, Claude-M. Viallet
Hex systems were recently introduced [A. P. Kels. Integrable systems on hexagonal lattices and consistency on polytopes with quadrilateral and hexagonal faces. 2022. arXiv:2205.027…
Bi-rational maps in four dimensions with two invariants
G. Gubbiotti, N. Joshi, D. T. Tran +1
In this paper we present a class of four-dimensional bi-rational maps with two invariants satisfying certain constraints on degrees. We discuss the integrability properties of thes…
On the algebraic structure of rational discrete dynamical systems
Claude M. Viallet
We show how singularities shape the evolution of rational discrete dynamical systems. The stabilisation of the form of the iterates suggests a description providing among other thi…
Algebraic entropy for differential-delay equations
Claude M. Viallet
We extend the definition of algebraic entropy to a class of differential-delay equations. The vanishing of the entropy, as a structural property of an equation, signals its integra…
From Yang-Baxter maps to integrable quad maps and recurrences
B. Grammaticos, A. Ramani, C-M. Viallet
Starting from known solutions of the functional Yang-Baxter equations, we exhibit Miura type of transformations leading to various known integrable quad equations. We then construc…
Weak Lax pairs for lattice equations
Jarmo Hietarinta, Claude Viallet
We consider various 2D lattice equations and their integrability, from the point of view of 3D consistency, Lax pairs and Bäcklund transformations. We show that these concepts, whi…