Algebraic Entropy for lattice equations

Abstract

We give the basic definition of algebraic entropy for lattice equations. The entropy is a canonical measure of the complexity of the dynamics they define. Its vanishing is a signal of integrability, and can be used as a powerful integrability detector. It is also conjectured to take remarkable values (algebraic integers).

Cited by in corpus (2)

• Discrete nonlinear hyperbolic equations. Classification of integrable cases
• A completeness study on a class of discrete, 'two by two' Lax pairs