Versions of the Closing Lemma for Certain Dynamical Systems on Tori

摘要: LetT n be then-torus. We show that strengthened versions of theC r -closing lemma (r≥1) take place for several classes dynamical systems on tori; namely, 1) Herman actions the groupZ k onT 1; 2) foliations without compact leaves 3; 3) diffeomorphisms ofT 1 with wandering chain recurrent points; 4) flows 2 trajectories and fixed points. also prove a version generalized interval exchange transformations under assumption nontrivially point has symbolic expansions sufficiently large, as corollary we get Closing similar in terms coding forC vector fields finitely many singularities saddle type an orientable surface genus≥2.