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- W4313208841 abstract "The $ (1+n) $-gon elliptic relative equilibrium (ERE for short) is the planar central configuration solution consisting of $ n $ unit masses at the vertices of a regular $ n $-gon with a body of mass $ m $ at the center, and each particle moves on a Keplerian orbit with a common eccentricity $ ein [0,1) $. Maxwell first considered this model in his study on the stability of the Saturn's rings. Moeckel [10] proves that for $ e = 0 $, the $ (1+n) $-gon is linearly stable for sufficiently large $ m $ for $ ngeq7 $. A natural question is that whether Moeckel's stability result holds for $ e>0 $. In the recent paper [2], Hu, Long and Ou give an affirmative answer for $ ngeq8 $, but the case $ n = 7 $ is difficult and still open. In this paper, we show that it is also true for $ n = 7 $, that is the $ (1+7) $-gon ERE is still linearly stable for any $ ein(0,1) $ when $ m $ is large enough." @default.
- W4313208841 created "2023-01-06" @default.
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- W4313208841 date "2023-01-01" @default.
- W4313208841 modified "2023-09-25" @default.
- W4313208841 title "Linear stability of the elliptic relative equilibrium with $ (1 + 7) $-gon central configuration in planar $ N $-body problem" @default.
- W4313208841 doi "https://doi.org/10.3934/dcds.2022162" @default.
- W4313208841 hasPublicationYear "2023" @default.
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