2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/114116Using invariance by fixed-endpoints homotopies and a generalized notion of symplectic Cayley transform, we prove a product formula for the Conley--Zehnder index of continuous paths with arbitrary endpoints in the symplectic group. We discuss two applications of the formula, to the metaplectic group and to periodic solutions of Hamiltonian systems.Symplectic GeometryMathematical Physicstext