On Geodesic Rays of Newtonian Gravitational Systems

Putian Yang; Shiqing Zhang

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arXiv · 2208.10066

On Geodesic Rays of Newtonian Gravitational Systems

Putian Yang·Shiqing Zhang

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Abstract

In this paper, we focus on the set of geodesics rays of the Newtonian N-body problem. We find that the limits of geodesic rays are also geodesic rays, hence they are not dense in the space of initial conditions. As a result, there are many motions whose domain is the half real line has non-negative total energy, and they are not geodesic rays, the set of such motions has positive measure, we think this set gives a large space to accommodate many solutions with "bad" behaviors. As an application of weak KAM theory for N-body problem, we give a brief proof of the existence of complete parabolic orbit starting from any given initial position.

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Putian Yang, Shiqing Zhang. 2022-08-22. On Geodesic Rays of Newtonian Gravitational Systems. https://arxiv.org/abs/2208.10066

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