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
Date:2017
Main Author: Percino-Figueroa, B.A.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
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
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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.
first_indexed 2025-11-25T10:20:24Z
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institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
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language English
last_indexed 2025-11-25T10:20:24Z
publishDate 2017
publisher Інститут математики НАН України
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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
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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