On the Maslov index of multi-pulse orbits
Résumé
Multi-pulse homoclinic orbits of Hamiltonian systems on $\mathbb R^4$ can be classified by a sequence of integers. In this paper, we find the surprising result that this string of integers encodes the value of the Maslov index of the homoclinic orbit. Our results include a computable formulation of the Maslov index for homoclinic orbits and a robust numerical method for the evaluation of the Maslov index.