The formation of periodic three-body orbits for Newtonian systems

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Table 4.

Fractal dimension for the distributions.

	v_in = 0			v_in = 2
Model	D_BSS	D_BB	D_TS	D_BSS	D_BB	D_TS
Figure-8	1.0	0.4	0.2	1.0	0.4	0.4
Model A	0.9	0.2	0.2	0.8	0.6	0.1
I.A.₄^i.c.(0.5)	1.2	0.1	0.3	1.1	0.5	0.4
$I . A ._{68}^{i . c .} (0.5)$ $Mathematical equation: $ I.A.^{i.c.}_{68}(0.5) $$	0.9	0.2	0.2	0.8	0.3	0.3

Notes. Fractal (box counting) dimension for the distributions over azimuth and polar angles for the various simulation outcomes for braids Figure-8, model A, I.A.₄^i.c.(0.5), and $I . A ._{68}^{i . c .} (0.5)$ $Mathematical equation: $ I.A.^{i.c.}_{68}(0.5) $$ (as in Table 3). Here D_BSS, D_BB, and D_TS give the box counting dimension for the binary-single-single, binary-binary, and triple-single results. Note the value of D_ts for model A is indicated as an order of magnitude estimate, because the number of successful simulations was too small to make a reliable estimate of the fractal dimension.

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