Proof of a conjecture of E. Strömgren

The conjecture of Strömgren according to which, in the restricted problem, a class of doubly asymptotic orbits are limit members of families of periodic orbits is examined in the more general framework of analytic Hamiltonian system with two degrees of freedom. Sufficient conditions for the conjecture to become a theorem are established. Theses conditions amount to a transversality condition for the doubly asymptotic orbits and are likely to be verified in the cases considered in the literature of numerical explorations of the restricted problem.