Mauricio Peixoto

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Maurício Matos Peixoto (born April 15, 1921 in Fortaleza , † April 28, 2019 in Rio de Janeiro ) was a Brazilian mathematician who dealt with dynamic systems.

Peixoto was originally an engineer. He studied at the University of Rio de Janeiro (Escola Nacional de Engenharia) with a degree in civil engineering in 1943. He then taught mathematics at his engineering school. With Marília Chaves Peixoto (1921–1961), his future wife, he founded a mathematics seminar there. In 1953 he became a professor of rational mechanics there . In 1953 he founded the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio with his former fellow student Leopoldo Nachbin (1922–1993) (and with the support of the astronomer and mathematician Lélio Gama (1892–1981), the first director) he stayed connected for the rest of his career. In 1949 he attended the University of Chicago and in 1957/58 Princeton University , where he came into close contact with Solomon Lefschetz . There he became interested in the stability theory of dynamic systems (stimulated in part by the work of Russian mathematicians, to whom Lefschetz referred him, especially 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 and more dimensions and began his investigations into dynamic systems. Peixoto founded a Brazilian school of mathematicians who dealt with dynamic systems.

1964 to 1968 Peixoto was a professor at Brown University and 1973 to 1978 at the University of São Paulo . In 1991 he retired from IMPA, but remained active as Professor Emeritus.

Peixoto's theorem, named after him, emerged from his research , which is used to characterize structurally stable flows on surfaces (for example, there should only be a finite number of fixed points and these should all be hyperbolic). For this he received the Bunge Foundation Award in 1969.

In 1982 he introduced the concept of focal decomposition ( focal decomposition , originally from him sigma decomposition called) that a formalization of the concept of focal points. He also published about it with René Thom . The concept was used in the arithmetic of square shapes and Brillouin zones in solid state physics.

From 1975 to 1977 he was President of the Brazilian Mathematical Society and 1981 to 1991 of the Brazilian Academy of Sciences. He has been a member of the Brazilian National Science and Technology Council since 1996. In 1986 he received the Third World Academy of Sciences award.

Fonts

  • Editor 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., Vol. 45, 1959, pp. 633-636
  • Structural stability on two dimensional manifolds , Topology, Volume 1, Issue 2, 1962, pp. 101–121 (Peixoto's theorem)
  • with Pugh Structural Stability , Scholarpedia
  • A brief survey of focal decomposition , in Peixoto u. a. (Ed.) Dynamics, Games and Science I , Springer Verlag 2011

Web links

Individual evidence

  1. ↑ He was director of the IMPA from 1952 to 1965 and at the same time director of the national observatory from 1951 to 1967
  2. ^ Peixoto On end point boundary value problems , J. Diff. Eq., Vol. 44, 1982, pp. 273-280
  3. ↑ Ivan Kupka, Peixoto On the enumerative geometry of geodesics , in From Topology to Computation, Proceedings Smalefest , Springer Verlag 1993, p. 243
personal data
SURNAME Peixoto, Mauricio
ALTERNATIVE NAMES Peixoto, Mauricio Matos
BRIEF DESCRIPTION Brazilian mathematician
DATE OF BIRTH April 15, 1921
PLACE OF BIRTH Fortaleza
DATE OF DEATH April 28, 2019
Place of death Rio de Janeiro