Action-minimizing periodic and quasi-periodic solutions in the N-body problem

Kuo Chang Chen*, Tiancheng Ouyang, Zhihong Xia

*Corresponding author for this work

Research output: Contribution to journalArticle

11 Scopus citations

Abstract

Considering any set of n-positive masses, n > 3, moving in ℝ2 under Newtonian gravitation, we prove that action-minimizing solutions in the class of paths with rotational and reflection symmetries are collision-free. For an open set of masses, the periodic and quasi-periodic solutions we obtained contain and extend the classical Euler-Moulton relative equilibria. We also show several numerical results on these action-minimizing solutions. Using a natural topological classification for collision-free paths via their braid types in a rotating frame, these action-minimizing solutions change from trivial to non-trivial braids as we vary masses and other parameters.

Original languageEnglish (US)
Pages (from-to)483-497
Number of pages15
JournalMathematical Research Letters
Volume19
Issue number2
DOIs
StatePublished - Jan 1 2012

ASJC Scopus subject areas

  • Mathematics(all)

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