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.
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 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.
↑ Pugh, Charles C. (1967). "An Improved Closing Lemma and a General Density Theorem". American Journal of Mathematics. 89 (4): 1010–1021. doi:10.2307/2373414. ISSN0002-9327. JSTOR2373414.
↑ Wandering points were introduced by George Birkhoff to describe dissipative systems (with chaotic behavior). In the case of a dynamical system given by a map f, a point wanders if it has a neighborhood U which is disjoint to all of the iterations of the map on it:
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