A restricted charged four-body problem

We consider a restricted charged four body problem which reduces to a two degrees of freedom Hamiltonian system, and prove the existence of infinite symmetric periodic orbits with arbitrarily large extremal period. Also, it is shown that an appropriate restriction of a Poincaré map of the system is conjugate to the shift homeomorphism on a certain symbolic alphabet.Partially supported by a grant of the CGICT no. P1386-0351.On leave of absence from Departamento de Fisica, Universidade de Lisboa. Partially supported by a grant of Fundaçao Calouste Gulbenkian no. 32/85/13.