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

In this work, Fatou studied for the first time the Poisson integral of an arbitrary measure on the unit circle.

This theorem was at the origin of a large body of research in 20th-century mathematics under the name of bounded analytic functions.

Some of the basic results of holomorphic dynamics were also independently obtained by Gaston Julia and Samuel Lattes in 1918.

[7] Holomorphic dynamics has experienced a strong revival since 1982 because of the new discoveries of Dennis Sullivan, Adrien Douady, John Hubbard and others.

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.