TY - JOUR
T1 - Action-minimizing periodic and quasi-periodic solutions in the N-body problem
AU - Chen, Kuo Chang
AU - Ouyang, Tiancheng
AU - Xia, Zhihong
PY - 2012
Y1 - 2012
N2 - 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.
AB - 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.
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U2 - 10.4310/MRL.2012.v19.n2.a19
DO - 10.4310/MRL.2012.v19.n2.a19
M3 - Article
AN - SCOPUS:84866701251
SN - 1073-2780
VL - 19
SP - 483
EP - 497
JO - Mathematical Research Letters
JF - Mathematical Research Letters
IS - 2
ER -