Bifurcations of Rough Heteroclinic Loops with Three Saddle Points

摘要

In this paper, we study the bifurcation problems of rough heteroclinic loups cormecting threcsaddle points for a higher-dimensional system. Under some transversal conditions and the nontwistedcondition. the existence. uniqueness. nd incoexistencc of thc l-heteroclinic loop with threc or twosaddle pomts. l-homoclinic orbit and l-periodic orbit near T are obtained. Nleanwhile, the bifurcationsurfaces and existence regions are also given. Moreover. the above bifurcation results are extended tothe case for heteroclinic loop with l saddle points.