263 citations · 921 across the 24 of their papers we have counts for
24 papers
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…
An exercise in experimental mathematics: calculation of the algebraic entropy of a map
C. M. Viallet
We illustrate the use of the notion of derived recurrences introduced earlier to evaluate the algebraic entropy of self-maps of projective spaces. We in particular give an example,…
On the degree growth of iterated birational maps
Claude M. Viallet
We construct a family of birational maps acting on two dimensional projective varieties, for which the growth of the degrees of the iterates is cubic. It is known that this growth…
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…