Dynamical systems with Newtonian type potentials. (English) Zbl 0667.70010

Degiovanni, Marco; Giannoni, Fabio; Marino, Antonio

Atti Accad. Naz. Lincei, VIII. Ser., Rend., Cl. Sci. Fis. Mat. Nat. 81, No. 3, 271-278 (1987).

We study the existence of regular periodic solutions to some dynamical systems whose potential energy is negative, has only a singular point and goes to zero at infinity. We give sufficient conditions to the existence of periodic solutions of assigned period which do not meet the singularity.

MSC:

70F99	Dynamics of a system of particles, including celestial mechanics
37-XX	Dynamical systems and ergodic theory
70C20	Statics

Keywords:

Newtonian potential; existence of regular periodic solutions; dynamical systems; existence of periodic solutions