ABSTRACT
It has been known for a long time that the T-periodic solutions of a Hamil tonian system
on the space of smooth T-periodic loops. To use this variational principle ef fectively, it is necessary to extend the above functional on a suitable Sobolev space. Critical points of such a functional will be classical T-periodic so lutions of the Hamiltonian system. Although they have an infinite Morse index and co-index, the concepts introduced in Chapter 2 will allow us to introduce a finite relative Morse index. The main result will be that such an index coincides with the Maslov index of the linearized system along the solution.
