We propose a survey of a forthcoming paper, concerning the study of the N-centre problem on the plane. In particular, we associate an anisotropic potential to every centre and our idea is to provide non-collision periodic trajectories in negative energy shells. This will be made through a double technique, which includes both variational and perturbation methods. The chaotic behaviour of the system is finally suggested by the presence of a symbolic dynamics.
The planar anisotropic N-centre problem at negative energies
Canneori G. M.
2020-01-01
Abstract
We propose a survey of a forthcoming paper, concerning the study of the N-centre problem on the plane. In particular, we associate an anisotropic potential to every centre and our idea is to provide non-collision periodic trajectories in negative energy shells. This will be made through a double technique, which includes both variational and perturbation methods. The chaotic behaviour of the system is finally suggested by the presence of a symbolic dynamics.
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