In the following paper https://arxiv.org/pdf/math/0408280.pdf there is created an isomorphism between the Floer Homology of an hamiltonian functional $H$ in the cotangent bundle and the the Morse homology of it's legendrian dual in the tangent bundle.
Now in part of creating this we associated to an orbit of $H$ an index that is the Maslov index and we wish to relate with the Morse index of the corresponding orbit of the legendrian dual. This is Theorem $2.1$ in the paper and they refer to another paper for the result. They claim the proof is done in Proposition $6.3$ of https://people.math.ethz.ch/~salamon/PREPRINTS/spec.pdf. Now what is really done here is that we are able to relate the Morse index of the orbit $q$ of the legendrian dual with the Maslov index given by the Lagrangian path created by the fundamental solution of a Jacobi-type equation and it's derivative. Now I believe we would want to relate this Lagrangian path given by the fundamental solution with the Lagrangian path used in the definition of the Maslov index of a an orbit $x$ of $H$ that gives us the orbit $q$ of the legendrian dual. Now I am having some difficulty seeing how we can relate these things and so any help regarding this and seeing how these things are actually related is appreciated.
Thanks in advance.
