Pierre Fatou

Pierre Joseph Louis Fatou (28 February 1878 – 9 August 1929 ) was a French mathematician and astronomer. He is known for major contributions to several branches of analysis. The Fatou lemma and the Fatou set are named after him.

Biography

Pierre Fatou's parents were Prosper Ernest Fatou (1832–1891) and Louise Eulalie Courbet (1844–1911), both of whom were in the military.

He was in friendly relations with several contemporary French mathematicians, especially, Maurice René Fréchet and Paul Montel.

In the summer of 1929 Fatou went on holiday to Pornichet, a seaside town to the west of Nantes. He was staying in Le Brise-Lames Villa near the port and it was there at 8 p.m. on Friday 9 August that he died in his room. See also the Wikipedia article on functions of bounded type.

A number of fundamental results on the analytic continuation of a Taylor series belong to Fatou.

investigated by Fatou in 1906. This picture is made with a modern computer.

z+1+e−z investigated by Fatou in 1926

of a sine function studied by Fatou in 1926

In 1917–1920 Fatou created the area of mathematics which is called holomorphic dynamics . It deals with a global study of iteration of analytic functions. He was the first to introduce and study the set which is called now the Julia set. (The complement of this set is sometimes called the Fatou set). Some of the basic results of holomorphic dynamics were also independently obtained by Gaston Julia and Samuel Lattes in 1918. Holomorphic dynamics has experienced a strong revival since 1982 because of the new discoveries of Dennis Sullivan, Adrien Douady, John Hubbard and others. In 1926, Fatou pioneered the study of dynamics of transcendental entire functions , a subject which is intensively developing at this time.

As a byproduct of his studies in holomorphic dynamics, Fatou discovered what are now called Fatou–Bieberbach domains . These are proper subregions of the complex space of dimension n, which are biholomorphically equivalent to the whole space. (Such regions cannot exist for n=1.)

Fatou did important work in celestial mechanics. He was the first to prove rigorously a theorem (conjectured by Gauss) on the averaging of a perturbation produced by a periodic force of short period . This work was continued by Leonid Mandelstam and Nikolay Bogolyubov and his students and developed into a large area of modern applied mathematics. Fatou's other research in celestial mechanics includes a study of the movement of a planet in a resisting medium.

Selected publications ;