[4][5] He entered the École Normale Supérieure in 1975, and completed an agrégation in mathematics in 1977.

[6] After completing military service in Brazil, he completed his PhD under Michael Herman in 1985 at Centre de mathématiques Laurent-Schwartz, which is a research unit jointly operated by the French National Center for Scientific Research (CNRS) and École Polytechnique.

[6][7][8] He took up a position at the University of Paris-Sud in 1987, and became a professor at the Collège de France in 1997, where he remained until his death.

[11][10] He joined the French Academy of Sciences and Brazilian Academy of Sciences in 1994, became a chevalier in the French Legion of Honor in 1995, and was awarded the Grand Cross of the Brazilian National Order of Scientific Merit in 1998.

His contributions include advances to KAM theory, and the introduction of the method of Yoccoz puzzles, a combinatorial technique which proved useful to the study of Julia sets.