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Ricardo Mañé Ramírez

Ricardo Mañé Ramírez, Uruguayan / Brazilian mathematician (Montevideo 14 January 1948 –Montevideo 09 March 1995)
 
World leader on dynamical systems
Authored 51 works with 1,333 citations
His book Introdução de teoria ergódica (Ergodic theory and differentiable dynamics) was translated into English language (1987) 

Showed that normal hiperbolicity is required for persistence of invariant manifolds (1974)

Defined quasi-Anosov diffeomorphisms

Proved that the interior in the C1 topology of the set of expansive diffeomorphisms is the set of quasi-Anosov diffeomorphisms (1975)

Proved that a compact metric space exhibiting expansive homeomorphisms must be finite dimensional and every minimal set of such homeomorphisms is zero dimensional  (1979)


 

INTRODUCED

With Paulo Sad & Sullivan the concept of holomorphic motion of a closed planar set (1983)

Notion of critical value independently from other authors

Notion of generic Lagrangian function 

Concept of ergodic closing lemma
Proved the stability conjecture for C1 class diffeomorphisms (1988)


EPONYMY

Mañé theorem 

Mañé-Mather set

Bochi-Mañé theorem

Holder-Mañé theorem

Mañé potential

Mañé supercritical hypersurfaces

Mañé conjecture

Araujo-Mañé theorem

Takens-Mañé theorem

Mañé ergodic closing lemma

Mañé-Sad-Sullivan theorem

Mañé-Conze-Guivarc’h lemma

Mañé critical values

Aubry-Mañé sets

Mañé hyperbolicity theorem

Mañé projection

Mañé-Lyubich measure

Bowen-Mañé phenomenon 

Mañé genericity theorem


HONOURS 

Two-time invited lecturer at International Congress of Mathematicians (1983 & 1994)