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Linear stability of the criss-cross orbit in the equal-mass three-body problem

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  • In this paper, we study the linear stability of the criss-cross orbit in the planar equal-mass three-body problem. In each period of the criss-cross orbit, the configurations of three masses are switching from a straight line to an isosceles triangle eight times. By analyzing its symmetry properties and variational characterization, we show that the criss-cross orbit is linearly stable via index theory.
    Mathematics Subject Classification: Primary: 70F07; Secondary: 70F10, 53D12.

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