Global Classification of Two-Component Approximately Integrable Evolution Equations

We globally classify two-component evolution equations, with homogeneous diagonal linear part, admitting infinitely many approximate symmetries. Important ingredients are the symbolic calculus of Gel'fand and Dikiǐ, the Skolem-Mahler-Lech theorem, an algorithm of Smyth, and results on diophantine equations in roots of unity obtained by Beukers.