A Cl closing lemma for equivariant endomorphisms under actions of finite groups

A C^l closing lemma is proved for equivariant endomorphisms under actions of finite groups. Our result shows that, for such an endomorphism, a nonwandering orbit together with its symmetric conjugates can be closed up under a Cl-small equivariant perturbation Project partially supported by the National Natural Science Foundation of China (Grant No. 19531070).