| Abstract: |
| The figure-eight solution and slalom solutions are
periodic solutions to equal-mass planar three-body problem
with vanishing angular momentum.
They are called `choreographic`
because three bodies chase each other on a single orbit with equal time delay.
Slalom solutions are classified by an integer $k$.
The $k=5$ slaloms belong to the same homotopy class with five iterations of the figure-eight.
Three $k=5$ slalom solutions are known under Newton potential.
We continue the figure-eight and slalom solutions to homogeneous potential $1/r^\alpha$.
Linear stability and Morse index of them are investigated.
Behavior of action integral near bifurcation points are closely examined. |
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