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Relating the morseMorse index with the Maslov index

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 morseMorse homology of it's legenderianlegendrian 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 morseMorse 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 morseMorse 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.

Relating the morse index with the Maslov index

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 legenderian 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.

Relating the Morse index with the Maslov index

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.

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Relating the morse index with the Maslov index

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 legenderian 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.