Periodic orbits of a one-dimensional non-autonomous Hamiltonian system

In this paper we study the properties of the periodic orbits of with x S1 and a T0 periodic potential. Called the frequency of windings of an orbit in S1 we show that exists an infinite number of periodic solutions with a given ρ. We give a lower bound on the number of periodic orbits with a given period and ρ by means of the Morse theory.