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Cesar Leopoldo Camacho

Cesar Leopoldo Camacho Manco, Peruvian-born Brazilian mathematician (Lima 15 April 1943 –


Internationally respected as one of great names in the field of complex dynamical systems 


ACHIEVEMENTS 

Established the essential analytic and geometric properties of solutions of complex differential equations

Proposed a generalization of theory of real dynamical systems in his doctoral thesis 

Established a generalization of Poincaré-Bendixson theorem (1973)

Defined the concept of hyperbolic fixed point of an action (1973)

Demonstrated that local structural stability is not a generic property for fields of lineal complex vectors and established a complete topological classification of these fields (1978)

With A. Lins Neto introduced the notion of regular homogenous forms (1982)

With A. Lins Neto & P. Sad introduced a class of foliations that share the reduction of singularities with their curve of separatrices or generalized curve-type foliations (1984)

With B. A. Scárdua determined a model differential equation which generalizes the Riccati equation (1999)

With L.H. Figueiredo first introduced computational methods for studying asymptotic behavior of solutions (2001)

With B. Scárdua characterized projective foliations that permit first liouvillian integrals

With B. Scárdua & H. Mosavati enunciated a theorem showing the moduli of Stein surface singularities (2008)

With B. Scárdua presented a Darboux-type theorem for germs of holomorphic one-dimensional foliations (2014)


EPONYMY

Camacho-Sad separatrix theorem

Camacho-Sad index theorem (1982)

Camacho-Sad índices

Camacho-Sad localization

Camacho-Chaperon hyperbolic condition (1971)

Camacho theorem (1978)

Camacho-Movasati-Sad index theorem

Camacho-Lehmann theorem for holomorphic foliations