Charles C. Pugh

This article is about the mathematician. For other people with the same name, see Charles Pugh (disambiguation).

Charles Chapman Pugh (born June 16, 1940) is an American mathematician who researches dynamical systems. Pugh received his PhD under Philip Hartman of Johns Hopkins University in 1965, with the dissertation The Closing Lemma for Dimensions Two and Three.^[1] He has since been a professor, now emeritus, at the University of California, Berkeley.

Charles C. Pugh
Charles Pugh, Berkeley, 1993
Born	(1940-06-16) June 16, 1940 (age 85) United States
Alma mater	Johns Hopkins University (PhD)
Known for	Work in dynamical systems
Scientific career
Fields	Mathematics
Institutions	University of California, Berkeley
Thesis	The Closing Lemma for Dimensions Two and Three  (1965)
Doctoral advisor	Philip Hartman
Doctoral students	Martin M. Wattenberg Amie Wilkinson
Website	https://math.berkeley.edu/people/faculty/charles-c-pugh

In 1967, he published a closing lemma named after him in the theory of dynamical systems.^[2][3] The lemma states: Let f be a diffeomorphism of a compact manifold with a nonwandering point x.^[4] Then, there is (in the space of diffeomorphisms, equipped with the ${\displaystyle C^{1}}$ topology) in a neighborhood of f a diffeomorphism g for which x is a periodic point. That is, by a small perturbation of the original dynamical system, a system with periodic trajectory can be generated.

In 1970, he was an invited speaker at the International Congress of Mathematicians in Nice, delivering a talk on Invariant Manifolds.

Mary Cartwright (left) with Charles Pugh, Nice, 1970

Books

• Real Mathematical Analysis, Springer-Verlag, 2002