Closed orbits of fixed energy for singular Hamiltonian systems (Q1173693)

The paper studies the classical \(N\)-dimensional Newtonian equations of motion in a potential field on an energy surface. The assumptions are that the potential is \(C^2\) away from the origin where it has a singularity. If the potential behaves like \(-|x|^{-a}\) with \(a>2\) the existence of periodic solutions without collisions is proved. If the potential behaves like \(-|x| ^{-b}\) with \(0<b<2\) the existence of periodic solutions that can pass through the collision is proved.