The C¹ closing lemma for nonsingular endomorphisms equivariant under free actions of finite groups

In this paper a closing lemma for C¹ nonsingular endomorphisms equivariant under free actions of finite-groups is proved. Hence a recurrent trajectory, as well as all of its symmetric conjugates, of a C¹ nonsingular cndomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small C¹ equivariant perturbation.