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Periodic solutions bifurcated from figure-eight choreographies of the equal mass three-body problem

Hiroshi FUKUDA

(2019.01.09)

Preprint arXiv:1901.00115


The following movies are periodic solutions bifurcated from the figure-eight choreographic solutions to the equation of motion

d2qi/dt2 = -∂U/∂qi, Ui>ju(qi-qj), i = 0,1,2
See arXiv:1901.00115 on initial conditions.

Homogeneous potential

u(r)=-1/ra

Dxy bifurcated from a=0.9966

a=0.9766

, Δt=T/12/, T=1

a=1.0166

, Δt=T/12/, T=1

a=1.0000 (Simó's H)

, Δt=T/12/, T=1

Bifurcation from a=1.3424

Dx at a=1.3425

, Δt=T/12/, T=1

D2 at a=1.3425

, Δt=T/12/, T=1

The Lennard-Jones-type potential

u(r)=-1/r6+1/r12

Dxy from α+ at T=16.878

From the left side

, Δt=T/12/, T=20

From the right side

, Δt=T/12/, T=20

Dxy from α- at T=14.836

From the left side

, Δt=T/12/, T=20

From the right side

, Δt=T/12/, T=20

Bifurcation from α+ at T=16.111

Dx

, Δt=T/12/, T=20

D2

, Δt=T/12/, T=20

Bifurcation from α- at T=14.861

Dx

, Δt=T/12/, T=20

D2

, Δt=T/12/, T=20

Cx bifurcated from α- at T=14.595

, Δt=T/12/, T=20

C2 bifurcated from α+ at T=18.615

, Δt=T/12/, T=20

Cy bifurcated from α+ at T=17.132

, Δt=T/12/, T=20