© 2015, Springer Basel. 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 (Formula Presented.) such that this system possesses no τ/2-antiperiodic solution for all (Formula Presented.), at least one τ/2-antiperiodic solution when (Formula Presented.), precisely 2n families of τ/2-antiperiodic circular solutions when (Formula Presented.), and precisely 2n+1 families of τ/2-antiperiodic circular solutions when (Formula Presented.). Each of these circular solution families is of dimension n - 1 module the S1-action.
- Anisotropic Lennard-Jones potential
- Circular periodic solutions
- Lennard-Jones potential