Charles C. Pugh

Charles Chapman Pugh, born on 16 June 1940, is an American mathematician who researches dynamical systems and is now professor emeritus at the University of California, Berkeley. He received his doctorate from Johns Hopkins University in 1965 under Philip Hartman, with a dissertation titled The Closing Lemma for Dimensions Two and Three. In 1967 he published the closing lemma that bears his name in the theory of dynamical systems. It says that when a diffeomorphism of a compact manifold has a nonwandering point, a small perturbation in the C1 topology produces a diffeomorphism for which that point is periodic, so a small change to the system can generate a periodic trajectory. In 1970 he was an invited speaker at the International Congress of Mathematicians in Nice, where he spoke on invariant manifolds. He is also the author of the textbook Real Mathematical Analysis, whose second edition appeared from Springer in 2015.