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.
Pierre Fatou's parents were Prosper Ernest Fatou (1832-1891) and Louise Eulalie Courbet (1844-1911), both of whom were in the military. Pierre's family would have liked for him to enter the military as well, but his health was not sufficiently good for him to pursue a military career.
Fatou entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an intern (stagiaire) in the Paris Observatory. Fatou was promoted to assistant astronomer in 1904 and to astronomer (astronome titulaire) in 1928. He worked in this observatory until his death.
Fatou was awarded the Becquerel prize in 1918; he was a knight of the Legion of Honour (1923). He was the president of the French mathematical society in 1927.
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. No cause of death was given on the death certificate but Audin argues that he died as a result of a stomach ulcer that burst. Fatou's nephew Robert Fatou wrote:
Having never thought it useful during his life to consult a doctor, my dear uncle died suddenly in a hotel room in Pornichet.
Fatou's funeral was held on 14 August in the church of Saint-Louis, and he was buried in the Carnel Cemetery in Lorient.
Fatou's work had very large influence on the development of analysis in the 20th century.
Fatou's PhD thesis Séries trigonométriques et séries de Taylor was the first application of the Lebesgue integral to concrete problems of analysis, mainly to the study of analytic and harmonic functions in the unit disc.
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Gaston Maurice Julia (3 February 1893 – 19 March 1978) was a French Algerian mathematician who devised the formula for the Julia set. His works were popularized by French mathematician Benoit Mandelbrot; the Julia and Mandelbrot fractals are closely related. He founded, independently with Pierre Fatou, the modern theory of holomorphic dynamics. Julia was born in the Algerian town of Sidi Bel Abbes, at the time governed by the French. During his youth, he had an interest in mathematics and music.
Complex dynamics, or holomorphic dynamics, is the study of dynamical systems obtained by iterating a complex analytic mapping. This article focuses on the case of algebraic dynamics, where a polynomial or rational function is iterated. In geometric terms, that amounts to iterating a mapping from some algebraic variety to itself. The related theory of arithmetic dynamics studies iteration over the rational numbers or the p-adic numbers instead of the complex numbers.
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 with the property that all nearby values behave similarly under repeated iteration of the function, and the Julia set consists of values such that an arbitrarily small perturbation can cause drastic changes in the sequence of iterated function values.