Department of Applied Mathematics, Tsinghua University, Beijing 100084, P.R. China ; School of Mathematical Science, Peking University, Beijing 1000871, P.R. China
Abstract:
In this paper a closing lemma for 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 nonsingular endomorphism equivariant under a free action of a finite group can be closed up simultaneously by an arbitrarily small equivariant perturbation.