摘要：By using the linear independent fundamental solutions of the linear variational equation along the heteroclinic loop to establish a suitable local coordinate system in some small tubular neighborhood of the heteroclinic loop, the Poincaré map is constructed to study the bifurcation problems of a fine 3-point loop in higher dimensional space. Under some transversal conditions and the non-twistedcond ition, the existence, coexistence and incoexistence of 2-point-loop, 1-homoclinic orbit, simple 1-periodic orbit and 2-fold 1-periodic orbit, and the number of 1-periodic orbits are studied. Moreover,the bifurcation surfaces and existence regions are given. Lastly, the above bifurcation results are applied to a planar system and an inside stability criterion is obtained.

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