2006/09/15 by Claude Viallet, Viallet, Claude
Mathematics · Physics and Astronomy · #Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.MP #nlin.SI
paper · pdf · doi:10.48550/arxiv.math-ph/0609043
arxiv created 2006/09/20 · arxiv updated 2009/12/01
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).