2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/67003Flows on (or variations of) discrete curves in $\R^2$ give rise to flows on a subalgebra of functions on that curve. For a special choice of flows and a certain subalgebra this is described by the Toda lattice hierachy. In the paper it is shown that the canonical symplectic structure on $\R^{2N}$, which can be interpreted as the phase space of closed discrete curves in $\R^2$ with length $N,$ induces Poisson commutation relations on the above mentioned subalgebra which yield the tri-hamiltonian poisson structure of the Toda lattice hierachy.Differential GeometrySymplectic Geometry52C99;53D17;70H06 (primary) 53Z02 (secondary)text