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...

Full description

Saved in:
Bibliographic Details
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
Tags: Add Tag
No Tags, Be the first to tag this record!
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.

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Description
Summary: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.
ISSN:1815-0659