BIFURCATIONS OF HOMOCLINIC LOOPS OF SADDLE EQUILIBRIUM STATES

The following sections are included:

• Stability of a separatrix loop on the plane

• Bifurcation of a limit cycle from a separatrix loop of a saddle with non-zero saddle value

• Bifurcations of a separatrix loop with zero saddle value

• Birth of periodic orbits from a homoclinic loop (the case dim W^u=1)

• Behavior of trajectories near a homoclinic loop in the case dim W^u > 1

• Codimension-two bifurcations of homoclinic loops

  • The case A = 0 — inclination-flip

  • The case Γ ⊂ W^SS — orbit-flip

  • The case σ = 0

• Bifurcations of the homoclinic-8 and heteroclinic cycles

• Estimates of the behavior of trajectories near a saddle equilibrium state