2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/61137Let ${\cal O}$ be the orbit of $η\in{\frak g}^*$ under the coadjoint action of the compact Lie group $G$. We give two formulae for calculating the action integral along a closed Hamiltonian isotopy on ${\cal O}$. The first one expresses this action in terms of a particular character of the isotropy subgroup of $η$. In the second one is involved the character of an irreducible representation of $G$.12 pages, LatexSymplectic Geometrytext