Pugh’s general density theorem

Let $M$ be a compact smooth manifold. There is a residual subset of $\operatorname{Diff}^{1}(M)$ in which every element $f$ satisfies $\overline{\operatorname{Per}(f)}=\Omega(f)$ . In other words: Generically, the set of periodic points of a $\mathcal{C}^{1}$ diffeomorphism is dense in its nonwandering set.

Here, $\operatorname{Diff}^{1}(M)$ denotes the set of all $\mathcal{C}^{1}$ difeomorphisms from $M$ to itself, endowed with the (strong) $\mathcal{C}^{1}$ topology.

References

1 Pugh, C., An improved closing lemma and a general density theorem, Amer. J. Math. 89 (1967).

Title	Pugh’s general density theorem
Canonical name	PughsGeneralDensityTheorem
Date of creation	2013-03-22 13:40:42
Last modified on	2013-03-22 13:40:42
Owner	Koro (127)
Last modified by	Koro (127)
Numerical id	8
Author	Koro (127)
Entry type	Theorem
Classification	msc 37C20
Classification	msc 37C25
Synonym	general density theorem