In mathematics, Pugh's closing lemma is a result that links periodic orbit solutions of differential equations to chaotic behaviour. It can be formally stated as follows:
- 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 .
Read more about Pugh's Closing Lemma: Interpretation, See Also
Famous quotes containing the words pugh and/or closing:
“[They] exchanged the quick, brilliant smile of women who dislike each other on sight.”
—Marshall Pugh (b. 1925)
“Our two eyes do not make our lot better; one serves us to see the good things, the other the evils of life. A lot of people have the bad habit of closing the first, and very few close the second.”
—Voltaire [François Marie Arouet] (1694–1778)