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Null Angular Momentum and Weak KAM Solutions of the Newtonian $N$-Body Problem
Symmetry, integrability and geometry: methods and applications, Tome 13 (2017) Cet article a éte moissonné depuis la source Math-Net.Ru

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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.
Keywords: $N$-body problem; angular momentum; free time minimizer; Hamilton–Jacobi equation. 
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     author = {Boris A. Percino-Figueroa},
     title = {Null {Angular} {Momentum} and {Weak} {KAM} {Solutions} of the {Newtonian} $N${-Body} {Problem}},
     journal = {Symmetry, integrability and geometry: methods and applications},
     year = {2017},
     volume = {13},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a67/}
}
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Boris A. Percino-Figueroa. Null Angular Momentum and Weak KAM Solutions of the Newtonian $N$-Body Problem. Symmetry, integrability and geometry: methods and applications, Tome 13 (2017). http://geodesic.mathdoc.fr/item/SIGMA_2017_13_a67/

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