Pierre Joseph Louis Fatou (28 February 1878, Lorient

Lorient

Lorient, or L'Orient, is a commune and a seaport in the Morbihan department in Brittany in north-western France.-History:At the beginning of the 17th century, merchants who were trading with India had established warehouses in Port-Louis...

 – 10 August 1929, Pornichet

Pornichet

Pornichet is a commune in the Loire-Atlantique department in western France.- Location :Pornichet is a coastal town of the Côte d'Amour, located a tens of kilometers west of Saint-Nazaire.The adjacent towns are Saint-Nazaire and La Baule-Escoublac....

) was a French

France

The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...

 mathematician

Mathematician

A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....

 working in the field of complex analytic dynamics. He entered the École Normale Supérieure

École Normale Supérieure

The École normale supérieure is one of the most prestigious French grandes écoles...

 in Paris

Paris

Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...

 in 1898 to study mathematics and graduated in 1901 when he was appointed an astronomy

Astronomy

Astronomy is a natural science that deals with the study of celestial objects and phenomena that originate outside the atmosphere of Earth...

 post in the Paris Observatory

Paris Observatory

The Paris Observatory is the foremost astronomical observatory of France, and one of the largest astronomical centres in the world...

. Fatou continued his mathematical explorations and studied iterative and recursive

Recursive

Recursive may refer to:*Recursion, the technique of functions calling themselves*Recursive function, a total computable function*Recursive language, a language which is decidable...

 processes like

, where Z is a number in the complex plane of the form , resulting in a series

Fatou was particularly interested in the case where , which was later analysed with computers by Benoît Mandelbrot

Benoît Mandelbrot

Benoît B. Mandelbrot was a French American mathematician. Born in Poland, he moved to France with his family when he was a child...

 to generate graphical representations of the behaviour of this series for each point, c, in the complex plane – now popularly called the Mandelbrot set

Mandelbrot set

The Mandelbrot set is a particular mathematical set of points, whose boundary generates a distinctive and easily recognisable two-dimensional fractal shape...

.

Fatou wrote many papers developing a Fundamental theory of iteration in 1917, which he published in the December 1917 part of Comptes Rendus. His findings were very similar to those of Gaston Maurice Julia

Gaston Julia

Gaston Maurice Julia was a French mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoît Mandelbrot; the Julia and Mandelbrot fractals are closely related....

, who submitted a paper to the Académie des Sciences in Paris for their 1918 Grand Prix on the subject of iteration from a global point of view. Their work is now commonly referred to as the generalised Fatou–Julia theorem.

See also

• Fatou's lemma
  Fatou's lemma
  In mathematics, Fatou's lemma establishes an inequality relating the integral of the limit inferior of a sequence of functions to the limit inferior of integrals of these functions...
  
  
• Fatou's theorem
  Fatou's theorem
  In complex analysis, Fatou's theorem, named after Pierre Fatou, is a statement concerning holomorphic functions on the unit disk and their pointwise extension to the boundary of the disk.-Motivation and statement of theorem:...
  
  
• Fatou set
• Fatou–Lebesgue theorem
  Fatou–Lebesgue theorem
  In mathematics, the Fatou–Lebesgue theorem establishes a chain of inequalities relating the integrals of the limit inferior and the limit superior of a sequence of functions to the limit inferior and the limit superior of integrals of these functions...
  
  
• Classification of Fatou components
  Classification of Fatou components
  In mathematics, if f = P/Q is a rational function defined in the extended complex plane, and ifthen for a periodic component U of the Fatou set, exactly one of the following holds:# U contains an attracting periodic point# U is parabolic...
  
  
• Fatou–Bieberbach domain

External links

• Pierre Fatou, mathématicien et astronome by Michèle Audin, on the site Images des Mathématiques.