Algebraic integrability of the Toda lattice \({\mathfrak d}^{(2)}_3\)
This paper studies the algebraic integrability of the Toda lattice associated with the affine Lie algebra \(\mathfrak{d}_{3}^{(2)}\). This is a polynomial dynamical system in a hyperplane of dimension 5 in \({\mathbb C}^{6}\) admitting 3 integrals of polynomial form. Using the Painlev'e divisors it is shown that this system is an algebraically integrable system. Furthermore a morphism between this system and the Mumford system is established.
scientific article; zbMATH DE number 5651247