MaurÃcio Peixoto
Maurício Matos Peixoto ( born April 15, 1921 in Fortaleza ) is a Brazilian mathematician who deals with dynamical systems.
Peixoto was originally an engineer. He studied at the University of Rio de Janeiro ( Escola Nacional de Engenharia ), graduating as a civil engineer in 1943. He then taught mathematics at his engineering school. With Marília Chaves Peixoto (1921-1961), his future wife, he founded a Mathematics Seminar. In 1953 he became a professor of rational mechanics. In 1953 he founded with his former fellow students Leopoldo Nachbin ( 1922 to 1993 ) ( and with the support of the astronomer and mathematician Lélio Gama ( 1892-1981 ), the first director ), the Instituto Nacional de Matemática Pura e Aplicada ( IMPA ) in Rio, with the he remained connected to the rest of his career. In 1949, he attended the University of Chicago and in 1957/58 Princeton University, where he joined in close association with Solomon Lefschetz. There he became interested in the stability theory of dynamical systems (partly inspired by the work of Russian mathematicians, the Lefschetz pointed out to him, particularly from the school of Lev Pontryagin ). There he also met Stephen Smale, who visited Rio in 1960, and there completed his proof of the generalized Poincaré conjecture in five or more dimensions, and began on Dynamical systems with its investigations. Peixoto founded a Brazilian school of mathematicians who dealt with dynamical systems.
1964 to 1968 he was a professor at Brown University and from 1973 to 1978 at the University of São Paulo. In 1991, he went at IMPA to retire, but remained active as professor emeritus.
He is known for the set of structurally stable Peixoto to characterize flows on surfaces ( for example, should only finitely many fixed points and these all be hyperbolic ). For this he received the 1969 Bunge Foundation Award.
In 1982 he introduced the concept of focal decomposition ( focal decomposition, originally called by him sigma decomposition) a, a formalization of the concept of focal points. He also published with René Thom. The concept was applied in the arithmetic of quadratic forms and Brillouin zones of solid state physics ( by Peixoto itself).
1975 to 1977 he was president of the Brazilian Mathematical Society from 1981 to 1991 and of the Brazilian Academy of Sciences. He was a member of the Brazilian national council for science and technology since 1996. In 1986 he was awarded the Third World Academy of Sciences.
Writings
- Publisher Dynamical Systems ( Conference, Salvador, Brazil, University of Bahia, July / August 1971), Academic Press 1973
- On structural stability, Annals of Mathematics, Volume 69, 1959, pp. 199-222
- Some examples on n- dimensional structural stability, Proc. Nat. Acad. Sci., Volume 45, 1959, pp. 633-636
- Structural stability on two dimensional manifolds, Topology, Volume 2, 1962, pp. 101-121 ( set of Peixoto )
- With Pugh Structural Stability, Scholarpedia
- A brief survey of focal decomposition, in Peixoto, among others (Eds.) Dynamics, Games and Science I, Springer Verlag 2011