Pugh’s closing lemma

Let f:MM be a 𝒞1 diffeomorphismMathworldPlanetmath of a compact smooth manifold M. Given a nonwandering point x of f, there exists a diffeomorphism g arbitrarily close to f in the 𝒞1 topology of Diff1(M) such that x is a periodic point of g.

The analogous theorem holds when x is a nonwandering point of a 𝒞1 flow on M.


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