Null Angular Momentum and Weak KAM Solutions of the Newtonian $N$-Body Problem

Symmetry Integrability and Geometry-Methods and Applications

article

Boris A. Percino-Figueroa¹ 

[1] Universidad Autónoma de Chiapas

关键词: N-body problem;    angular momentum;    free time minimizer;    Hamilton–Jacobi equation;   

DOI  :  10.3842/SIGMA.2017.068

来源: National Academy of Science of Ukraine

【 摘 要 】

In [ Arch. Ration. Mech. Anal. 213 (2014), 981-991] it has been proved that in the Newtonian $N$-body problem, given a minimal central configuration $a$ and an arbitrary configuration $x$, there exists a completely parabolic orbit starting on $x$ and asymptotic to the homothetic parabolic motion of $a$, furthermore such an orbit is a free time minimizer of the action functional. In this article we extend this result in abundance of completely parabolic motions by proving that under the same hypothesis it is possible to get that the completely parabolic motion starting at $x$ has zero angular momentum. We achieve this by characterizing the rotation invariant weak KAM solutions as those defining a lamination on the configuration space by free time minimizers with zero angular momentum.

【 授权许可】

Unknown