Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem
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, furthe...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2017 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2017
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/148745 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| _version_ | 1862546089614245888 |
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| author | Percino-Figueroa, B.A. |
| author_facet | Percino-Figueroa, B.A. |
| citation_txt | 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| description | 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.
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| first_indexed | 2025-11-25T10:20:24Z |
| format | Article |
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| id | nasplib_isofts_kiev_ua-123456789-148745 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-11-25T10:20:24Z |
| publishDate | 2017 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Percino-Figueroa, B.A. 2019-02-18T18:23:06Z 2019-02-18T18:23:06Z 2017 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. 1815-0659 2010 Mathematics Subject Classification: 37J15; 37J50; 70F10; 70H20 DOI:10.3842/SIGMA.2017.068 https://nasplib.isofts.kiev.ua/handle/123456789/148745 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. 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. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem Article published earlier |
| spellingShingle | Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem Percino-Figueroa, B.A. |
| title | Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem |
| title_full | Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem |
| title_fullStr | Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem |
| title_full_unstemmed | Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem |
| title_short | Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem |
| title_sort | null angular momentum and weak kam solutions of the newtonian n-body problem |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/148745 |
| work_keys_str_mv | AT percinofigueroaba nullangularmomentumandweakkamsolutionsofthenewtoniannbodyproblem |