Ricardo Mañé

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Ricardo Mañé Ramirez (born January 14, 1948 in Montevideo , † March 9, 1995 ibid) was a Uruguayan mathematician who dealt with the theory of dynamic systems and ergodic theory and worked in Brazil.

Life

Mañé studied at the University of Montevideo (with Jorge Lewowicz) and received his doctorate in 1973 with Jacob Palis at the Instituto Nacional de Matemática Pura e Aplicada (IMPA) in Rio de Janeiro. He researched and taught at IMPA.

In 1974 he showed that normal hyperbolicity is not only necessary for the persistence of invariant manifolds (as was already known from Morris Hirsch , Charles C. Pugh , Michael Shub ), but also sufficient. In 1988 he proved the presumption of stability for C1 diffeomorphisms . His Ergodic Closing Lemma was important for the proof. Various mathematical concepts are named after him. He is known for a book on ergodic theory within the theory of dynamic systems.

He wrote the sentence by Mañé-Bochi (1983).

In 1983 he was invited speaker at the International Congress of Mathematicians in Warsaw ( Oseledec's theorem from the general viewpoint ) and in 1994 in Zurich ( Ergodic variational methods: new techniques and new problems ).

Fonts

  • Persistent manifolds are normally hyperbolic, Bulletin AMS, Volume 80, 1974, pp. 90-91, Online (detailed under the same title in: Transactions AMS, Volume 246, 1978, pp. 261-283)
  • Expansive diffeomorphisms, Proceedings of the Symposium on Dynamical Systems (University of Warwick, 1974), Lect. Notes in Math. Vol. 468, Springer 1975, pp. 162-174
  • On the dimension of the compact invariant sets of certain non-linear maps, Springer, Lectures Notes in Math. Vol. 898, 1981, pp. 230-242.
  • An ergodic closing lemma, Annals of Mathematics, Second Series, Volume 116, 1982, pp. 503-540.
  • with P. Sad, D. Sullivan: On the dynamics of rational maps, Annales scientifiques de l'École Normale Supérieure, Volume 16, 1983, pp. 193-217
  • A proof of the C1 stability conjecture, Publications Mathématiques de l'IHÉS, Volume 66, 1987, pp. 161-210
  • On the topological entropy of geodesic flows, Journal of Differential Geometry, Volume 45, 1997, pp. 74-93.
  • Ergodic Theory and Differentiable Dynamics, Results of Mathematics and its Frontier Areas, Springer 1987

literature

  • Obituary Bulletin Brazilian Mathematical Society, Volume 29, 1998, No. 2
  • Homenagem a Ricardo Mañé, Revista Matemática Universitária, No. 18, 1995, pp. 1-18

Web links

Individual evidence

  1. ↑ See Mañé, Persistent manifolds are normally hyperbolic, Bulletin AMS, Volume 80, 1974, pp. 90-91
  2. ↑ See Christian Bonatti Pugh closing lemma, Scholarpedia
personal data
SURNAME Mané, Ricardo
ALTERNATIVE NAMES Mañé Ramirez, Ricardo (full name)
BRIEF DESCRIPTION Uruguayan mathematician
DATE OF BIRTH January 14, 1948
PLACE OF BIRTH Montevideo
DATE OF DEATH March 9, 1995
Place of death Montevideo