Pierre Fatou

Pierre Fatou

Pierre Joseph Louis Fatou (28 February 1878, Lorient – 10 August 1929, Pornichet) was a French mathematician working in the field of complex analytic dynamics. He entered the École Normale Supérieure in Paris in 1898 to study mathematics and graduated in 1901 when he was appointed an astronomy post in the Paris Observatory. Fatou continued his mathematical explorations and studied iterative and recursive processes like

$Z \to Z^2 + c \,\!$, where Z is a number in the complex plane of the form $Z=x+iy \,\!$, resulting in a series

$Z_0 = x+iy \,\!$

$Z_1 = Z_0^2+c \,\!$

$Z_2 = Z_1^2+c=(Z_0^2+c)^2+c = Z_0^4+2cZ_0^2+c^2+c\,\!$

$Z_3 = \cdots. \,\!$

Pierre Fatou was the first to define the Mandelbrot set.

Fatou was particularly interested in the case where Z₀ = 0, which was later analysed with computers by Benoît Mandelbrot to generate graphical representations of the behaviour of this series for each point, c, in the complex plane – now popularly called the Mandelbrot set.

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, 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 theorem
• Fatou set
• Fatou–Lebesgue theorem
• Classification of Fatou components
• Fatou–Bieberbach domain

References

• (fr) Michèle Audin (2009). Fatou, Julia, Montel, le Grand prix des sciences mathématiques de 1918, et après... Springer (Heidelberg) ISBN: 978-3-642-00445-2

External links

• O'Connor, John J.; Robertson, Edmund F., "Pierre Fatou", MacTutor History of Mathematics archive, University of St Andrews, http://www-history.mcs.st-andrews.ac.uk/Biographies/Fatou.html .
• Pierre Fatou, mathématicien et astronome by Michèle Audin, on the site Images des Mathématiques.

Persondata
Name	Fatou, Pierre
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Date of birth	28 February 1878
Place of birth
Date of death	10 August 1929
Place of death