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

Source abstract

In this paper a closing lemma for C 1 C^1 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 C 1 C^1 nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small C 1 C^1 equivariant perturbation.