Jean-Christophe Yoccoz (29 May 1957 – 3 September 2016) was a French

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

. He was awarded a

Fields Medal The Fields Medal is a prize awarded to two, three, or four mathematicians under 40 years of age at the International Congress of the International Mathematical Union (IMU), a meeting that takes place every four years. The name of the award h ...

in 1994, for his work on

dynamical system In mathematics, a dynamical system is a system in which a function describes the time dependence of a point in an ambient space. Examples include the mathematical models that describe the swinging of a clock pendulum, the flow of water i ...

Biography

Yoccoz attended the

Lycée Louis-le-Grand The Lycée Louis-le-Grand (), also referred to simply as Louis-le-Grand or by its acronym LLG, is a public Lycée (French secondary school, also known as sixth form college) located on rue Saint-Jacques in central Paris. It was founded in the ...

, during which time he was a silver medalist at the 1973

International Mathematical Olympiad The International Mathematical Olympiad (IMO) is a mathematical olympiad for pre- university students, and is the oldest of the International Science Olympiads. The first IMO was held in Romania in 1959. It has since been held annually, excep ...

and a gold medalist in 1974. He entered the

École Normale Supérieure École may refer to: * an elementary school in the French educational stages normally followed by secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing in région Île-de-France * École, S ...

in 1975, and completed an

agrégation In France, the ''agrégation'' () is a competitive examination for civil service in the French public education system. Candidates for the examination, or ''agrégatifs'', become ''agrégés'' once they are admitted to the position of ''profe ...

in mathematics in 1977. After completing military service in

Brazil Brazil ( pt, Brasil; ), officially the Federative Republic of Brazil (Portuguese: ), is the largest country in both South America and Latin America. At and with over 217 million people, Brazil is the world's fifth-largest country by area ...

, he completed his

PhD PHD or PhD may refer to: * Doctor of Philosophy (PhD), an academic qualification Entertainment * '' PhD: Phantasy Degree'', a Korean comic series * '' Piled Higher and Deeper'', a web comic * Ph.D. (band), a 1980s British group ** Ph.D. (Ph.D. al ...

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 Ecole polytechnique. He took up a position at the University of Paris-Sud in 1987, and became a professor at the

Collège de France The Collège de France (), formerly known as the ''Collège Royal'' or as the ''Collège impérial'' founded in 1530 by François I, is a higher education and research establishment ('' grand établissement'') in France. It is located in Paris n ...

in 1997, where he remained until his death. He was a member of Bourbaki. Yoccoz won the

Salem Prize The Salem Prize, in memory of Raphael Salem, is awarded each year to young researchers for outstanding contributions to the field of analysis. It is awarded by the School of Mathematics at the Institute for Advanced Study in Princeton and was fou ...

in 1988. He was an

invited speaker at the International Congress of Mathematicians This is a list of International Congresses of Mathematicians Plenary and Invited Speakers. Being invited to talk at an International Congress of Mathematicians has been called "the equivalent, in this community, of an induction to a hall of fame." ...

in 1990 at Kyoto, and was awarded the

at the

International Congress of Mathematicians The International Congress of Mathematicians (ICM) is the largest conference for the topic of mathematics. It meets once every four years, hosted by the International Mathematical Union (IMU). The Fields Medals, the Nevanlinna Prize (to be rena ...

in 1994 in

Zürich , neighboring_municipalities = Adliswil, Dübendorf, Fällanden, Kilchberg, Maur, Oberengstringen, Opfikon, Regensdorf, Rümlang, Schlieren, Stallikon, Uitikon, Urdorf, Wallisellen, Zollikon , twintowns = Kunming, San Francisco Z ...

. He joined the

French Academy of Sciences The French Academy of Sciences (French: ''Académie des sciences'') is a learned society, founded in 1666 by Louis XIV at the suggestion of Jean-Baptiste Colbert, to encourage and protect the spirit of French scientific research. It was at ...

and

Brazilian Academy of Sciences The Brazilian Academy of Sciences ( pt, italic=yes, Academia Brasileira de Ciências or ''ABC'') is the national academy of Brazil. It is headquartered in the city of Rio de Janeiro and was founded on May 3, 1916. Publications It publishes a lar ...

in 1994, became a chevalier in the

French Legion of Honor The National Order of the Legion of Honour (french: Ordre national de la Légion d'honneur), formerly the Royal Order of the Legion of Honour ('), is the highest French order of merit, both military and civil. Established in 1802 by Napoleon ...

in 1995, and was awarded the Grand Cross of the Brazilian National Order of Scientific Merit in 1998.

Mathematical work

Yoccoz's worked on the theory of

s, his contributions include advances to

KAM theory Kaam ( Gurmukhi: ਕਾਮ ''Kāma'') in common usage, the term stands for 'excessive passion for sexual pleasure' and it is in this sense that it is considered to be an evil in Sikhism. In Sikhism it is believed that Kaam can be overcom ...

, and the introduction of the method of Yoccoz puzzles, a combinatorial technique which proved useful to the study of

Julia set In the context of complex dynamics, a branch of mathematics, the Julia set and the Fatou set are two complementary sets (Julia "laces" and Fatou "dusts") defined from a function. Informally, the Fatou set of the function consists of values wi ...

Notable publications

* Yoccoz, J.-C. Conjugaison différentiable des difféomorphismes du cercle dont le nombre de rotation vérifie une condition diophantienne. Ann. Sci. École Norm. Sup. (4) 17 (1984), no. 3, 333–359. doi:10.24033/asens.1475 * Yoccoz, Jean-Christophe
Théorème de Siegel, nombres de Bruno et polynômes quadratiques. Petits diviseurs en dimension 1.
Astérisque No. 231 (1995), 3–88.

References

{{DEFAULTSORT:Yoccoz, Jean Christophe 1957 births 2016 deaths 20th-century French mathematicians 21st-century French mathematicians Fields Medalists Paris-Sud 11 University faculty École Normale Supérieure alumni Members of the Brazilian Academy of Sciences Recipients of the Great Cross of the National Order of Scientific Merit (Brazil) Lycée Louis-le-Grand alumni Members of the French Academy of Sciences International Mathematical Olympiad participants Dynamical systems theorists Nicolas Bourbaki