Abstract
Consideration is given to a system of differential equations which has two homoclinic solutions to a same saddle-focus point. The authors prove the existence of a subsystem of solutions which remain in a neighborhood of those homoclinic orbits. In addition to the upper and lower subsystem already described by L. Slinikov's (1965) theorem, this theorem contains solutions that switch in every turn from the neighborhood of one homoclinic to the neighborhood of the other. >
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