2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/120967The modular vector field plays an important role in the theory of Poisson manifolds and is intimately connected with the Poisson cohomology of the space. In this paper we investigate its significance in the theory of integrable systems. We illustrate in detail the case of the Toda lattice both in Flaschka and natural coordinates.16 pages, 29 references, to appear in Differential Geometry and its applicationsDifferential GeometryMathematical Physics53D17; 37J35text