On a product formula for the Conley--Zehnder index of symplectic paths   and its applications
  Using 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. 
Maurice de Gosson, Serge de Gosson, Paolo Piccione