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Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem
Репозиторій DSpace/Manakin
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2017, том 13
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Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem
Інший ID:
2010 Mathematics Subject Classification: 37J15; 37J50; 70F10; 70H20
DOI:10.3842/SIGMA.2017.068
DOI:10.3842/SIGMA.2017.068
Посилання:
Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem / B.A. Percino-Figueroa // Symmetry, Integrability and Geometry: Methods and Applications. — 2017. — Т. 13. — Бібліогр.: 12 назв. — англ.
Підтримка:
The author acknowledges the referees for their valuable suggestions and remarks that substantially improved this article. The author is grateful to Ezequiel Maderna for his advice, to H´ector
S´anchez Morgado for his suggestions and to Eddaly Guerra Velasco for her support in the process
of this research.
Дата:
2017
Переглядів:
511
Завантажень:
219
Анотація:
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.
