Periodic Solutions for the Generalized Anisotropic Lennard–jones Hamiltonian

We characterize the circular periodic solutions of the generalized Lennard–Jones Hamiltonian system with two particles in Rn, and we analyze what of these periodic solutions can be continued to periodic solutions of the anisotropic generalized Lennard–Jones Hamiltonian system. We also characterize the periods of antiperiodic solutions of the generalized Lennard–Jones Hamiltonian system on R2n, and prove the existences of 0 < τ∗ ≤ τ∗∗ such that this system possesses no τ/2-antiperiodic solution for all τ ∈ (0, τ∗), at least one τ/2-antiperiodic solution when τ = τ∗, precisely 2n families of τ/2-antiperiodic circular solutions when τ = τ∗∗, and precisely 2n+1 families of τ/2-antiperiodic circular solutions when τ > τ∗∗. Each of these circular solution families is of dimension n− 1 module the S1-action.