Connecting orbits for Newtonian-like \(N\)-body problems (Q264842)

The paper gives the existence of an orbit connecting the center of mass (or total collapse) and infinity for the \(n\)-body problem whose potential is an inverse power law with power between 0 and 2 (or weak force Newtonian potential). The connecting orbit is non-parabolic because the minimum of its kinetic energy is bounded away from zero. The existence of the connecting orbit is obtained, as a limit as the right endpoint of the time interval goes to infinity, of minimizers of a variational problem whose boundary conditions are the center of mass and a central configuration. The existence of the connecting orbit is an extension of earlier results and methods of \textit{C. Souissi} [An. Univ. Craiova, Ser. Mat. Inf. 31, 85--93 (2004; Zbl 1109.70007)] and \textit{S. Zhang} [Sci. China, Math. 55, No. 4, 721--725 (2012; Zbl 1322.70006)] for the Newtonian restricted three-body problem.