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

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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Main Author: Percino-Figueroa, B.A.
Format: Article
Language:English
Published: Інститут математики НАН України 2017
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/148745
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spelling irk-123456789-1487452019-02-19T01:29:48Z Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem Percino-Figueroa, B.A. 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. 2017 Article 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 http://dspace.nbuv.gov.ua/handle/123456789/148745 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
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.
format Article
author Percino-Figueroa, B.A.
spellingShingle Percino-Figueroa, B.A.
Null Angular Momentum and Weak KAM Solutions of the Newtonian N-Body Problem
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Percino-Figueroa, B.A.
author_sort Percino-Figueroa, B.A.
title 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_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_sort null angular momentum and weak kam solutions of the newtonian n-body problem
publisher Інститут математики НАН України
publishDate 2017
url http://dspace.nbuv.gov.ua/handle/123456789/148745
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.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT percinofigueroaba nullangularmomentumandweakkamsolutionsofthenewtoniannbodyproblem
first_indexed 2023-05-20T17:31:14Z
last_indexed 2023-05-20T17:31:14Z
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