Pugh’s closing lemma
Let be a diffeomorphism of a compact smooth manifold . Given a nonwandering point of , there exists a diffeomorphism arbitrarily close to in the topology of such that is a periodic point of .
The analogous theorem holds when is a nonwandering point of a flow on .
References
- 1 Pugh, C., An improved closing lemma
and a general density theorem, Amer. J. Math. 89 (1967).