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

d2qi/dt2 = -∂U/∂qi, U=Σi>ju(qi-qj), i = 0,1,2.

Legends

• f8: the figure-eight choreography under homogeneous interaction potential

• α± : the figure-eight choreography under Lennerd-Jones potential

• ↼: two-fold type bifurcation 

• ←: three-fold type bifurcation

• ⇐: six-fold type bifurcation  

• Indent level of movie: the generation of bifurcations from the figure-eight

• L: bifurcation from Left side 

• R: bifurcation from right side 

• Hi: higher action value 

• Lo: Lower action value

• Light grayed symbol: symbol used in preprint2019

• > button: stop movie at next T/n (initially n=12) 

• < button: stop movie at previous T/n (initially n=12) 

D2h{S,M,μ} ← f8 a=0.9966; Dxy 

D2{SM,μ} D2{CS,μ} ⇐ f8 a=1.3424

D2h{S,M,μ} ← α+ T=16.878; Dxy 

D2h{S,M,μ} ← α- T=14.836; Dxy 

D2{SM,μ} D2{CS,μ} ⇐ α+ T=16.111

D2{SM,μ} D2{CS,μ} ⇐ α- T=14.861

D6{μC,SM} ↼ α- T=14.595; Cx 

D6{μC,S} ↼ α+ T=18.615; C2 

C6h{CM,μ} ↼ α+ T=17.132; Cy