Pugh’s closing lemma
Let $f:M\to M$ be a ${\mathcal{C}}^{1}$ diffeomorphism^{} of a compact smooth manifold $M$. Given a nonwandering point $x$ of $f$, there exists a diffeomorphism $g$ arbitrarily close to $f$ in the ${\mathcal{C}}^{1}$ topology of ${\mathrm{Diff}}^{1}(M)$ such that $x$ is a periodic point of $g$.
The analogous theorem holds when $x$ is a nonwandering point of a ${\mathcal{C}}^{1}$ flow on $M$.
References
- 1 Pugh, C., An improved closing lemma^{} and a general density theorem, Amer. J. Math. 89 (1967).
Title | Pugh’s closing lemma |
---|---|
Canonical name | PughsClosingLemma |
Date of creation | 2013-03-22 14:07:13 |
Last modified on | 2013-03-22 14:07:13 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 8 |
Author | Koro (127) |
Entry type | Theorem |
Classification | msc 37C20 |
Classification | msc 37C25 |
Synonym | closing lemma |