2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56543We discuss in this paper the canonical structure of classical field theory in finite dimensions within the {\it{pataplectic}} hamiltonian formulation, where we put forward the role of Legendre correspondance. We define the Poisson $\mathfrak{p}$-brackets and $\mathfrakω$-brackets which are the analogues of the Poisson bracket on forms. We formulate the equations of motion of forms in terms of $\mathfrak{p}$-brackets and $\mathfrakω$-brackets with the $n$-form ${\cal H}ω$. As illustration of our formalism we present two examples: the interacting scalar fields and conformal string theory.minor modifications in the introduction and ref. added. (42 pages)Mathematical PhysicsGeneral Relativity and Quantum CosmologyHigh Energy Physics - TheoryDynamical Systemstext