Pierre Fatou

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Pierre Fatou

Pierre Joseph Louis Fatou (born February 28, 1878 in Lorient , † August 10, 1929 in Pornichet ) was a French mathematician .

life and work

After studying at the École normal supérieure in Paris from 1898 to 1900, he worked at the observatory in Paris from 1901 . In addition to his astronomical research, he delivered a variety of mathematical works and received his doctorate in mathematics in 1907 with a thesis on trigonometric series and Taylor series . This was one of the first applications of the Lebesgue integral to other problems of analysis. As early as 1906 he was investigating the iteration of certain rational functions . He later delved into the subject in more detail and published his extensive studies on iteration of rational functions in 1919 and 1920 (in three parts). Irrespective of this, such studies were also carried out by Gaston Julia at the same time . Fatou originally wanted to take part in the 1915 competition for the Academy of Sciences Prize, which was dedicated to this topic, and published the first results in the Comptes Rendus in December 1917. After Gaston Julia, who had come to similar results, published in a note in the Comptes Rendus registered priority claims in 1917 (he had previously deposited his work in a sealed envelope with the Academy), he refrained from doing so.

July amount of . Fatou showed in 1906 that it is a non-analytical Jordan curve.

The quantities that are fundamental in theory are now referred to as the fat quantity and the July quantity . Fatou and Julia defined these sets in different ways. Today practically all textbooks on complex dynamics, as the Fatou-Juliasche iteration theory is also called, follow the Fatous approach. Until the early 1980s, complex dynamics received relatively little attention, despite important contributions from Hubert Cremer , Carl Ludwig Siegel and others. Then the interest in it increased sharply, on the one hand due to the beautiful computer graphics of Juliamenet, which became known to a wide audience by Benoît Mandelbrot , Heinz-Otto Peitgen and others, on the other hand due to important new mathematical methods, which were introduced by Dennis Sullivan and Adrien Douady , John H. Hubbard, and other mathematicians.

When examining the iteration of functions of two complex variables, Fatou was led to the sets called Fatou-Bieberbach domains today . In 1926 he also examined the iteration of entire transcendent functions. Another important result of his work is Fatou's lemma and Fatou's theorem from his dissertation, which specifies the conditions when a holomorphic function defined in the open unit circle can be continued point by point to the boundary.

He also published on celestial mechanics , for example binary star systems . In 1928, a year before his death, he was awarded the title of astronomer. He was a member of the Legion of Honor.

He was a member of the Société Mathématique de France (SMF) from 1904 and its president in 1926.

literature

  • Michèle Audin : Fatou, Julia , Montel , le grand prix des sciences mathématiques de 1918, et après… Springer, 2009, ISBN 978-3-642-00445-2 . (French); English translation: Michèle Audin: Fatou, Julia, Montel, The Great Prize of Mathematical Sciences of 1918, and Beyond . Springer, 2011, ISBN 978-3-642-17853-5 .
  • Michèle Audin: Pierre Fatou, mathématicien et astronome , Images des Mathématiques, CNRS, 2009.
  • Daniel S. Alexander: A history of complex dynamics: from Schröder to Fatou and Julia. (Aspects of Mathematics), Vieweg, Braunschweig 1994, ISBN 3-528-06520-6 .
  • Daniel Alexander, Felice Iavernaro, Alessandro Rosa: Early days in complex dynamics: a history of complex dynamics in one variable 1906–1940 , History of Mathematics 38, American Mathematical Society 2012
  • Daniel Alexander, Robert L. Devaney: A century of complex dynamics . In A Century of Advancing Mathematics , Mathematical Association of America, 2015

Web links

Individual evidence

  1. Jump up ↑ Pierre Fatou: Séries trigonométriques et séries de Taylor , Acta Mathematica, Volume 30, 1906, pp. 335-400
  2. ↑ Pierre Fatou: Sur les solutions uniformes de certaines equations fonctionnelles , Comptes Rendus, Volume 143, 1906, pp. 546-548, online .
  3. ^ Pierre Fatou: Sur les equations fonctionelles . In: Bulletin de la Société Mathématique de France , Volume 47, 1919, pp. 161-271, Volume 48, 1920, pp. 33-94, 208-314, Online: Part 1 , Part 2 , Part 3
  4. ^ Heinz-Otto Peitgen, Peter Richter : The Beauty of Fractals . Springer, Berlin 1986, ISBN 3-540-15851-0 .
  5. ↑ Pierre Fatou: Sur l'itération des fonctions transcendantes entières , Acta Mathematica, Volume 47, 1926, pp. 337-370.
  6. ^ Fatou Theorem, Encyclopedia of Mathematics
personal data
SURNAME Fatou, Pierre
ALTERNATIVE NAMES Fatou, Pierre Joseph Louis (full name)
BRIEF DESCRIPTION French mathematician
DATE OF BIRTH February 28, 1878
PLACE OF BIRTH Lorient
DATE OF DEATH August 10, 1929
Place of death Pornichet