Fatou, Julia, Montel

Michèle Audin; Professor of Mathematics at IRMA, Université de Strasbourg et CNRS, France.

I The Great Prize, the framework.- I.1 The iteration problem in 1915.- I.2 The protagonists around 1917-1918.- I.3 The war.- I.4 Iteration, a few definitions and notation.- I.5 Normal families.- I.6 Relation to functional equations.- II The Great Prize of Mathematical.- II.1 Year 1917.- II.2 Year 1918.- III The memoirs.- III.1 Julia's memoir.- III.2 The (three) memoir(s) of Fatou.- III.3 Comments (in the first person).- III.4 To summarise.- IV After Fatou and Julia.- IV.1 Stop.- IV.2 Hausdorff distance (1914) and dimension (1919).- IV.3 Irregular points, J-points, O-points (1925-1927).- IV.4 The centre problem (1927-1942).-IV.5 Holomorphic dynamics.-V On Pierre Fatou.-V.1 Childhood and youth of Fatou.- V.2 What do we know of Pierre Fatou?.- V.3 Continuation of Fatou's career.- V.4 Fatou's thesis.- V.5 Fatou as a mathematician.-V.6 Fatou as an astronomer.- V.7 Teaching and candidatures of Fatou.- V.8 Fatou and other mathematicians.- V.9 Death of Fatou.- VI A controversy in 1965.- VI.1 The protagonists, from 1918 to 1965.- VI.2 Relations between Julia and Montel, in the 1930's.- VI.3 The third centenary of the Institut de France VI.4.- As a conclusion: O for a biography of Gaston Julia.- References.-Index.

From the book reviews:

"Book is a most welcome addition to the conversation involving complex dynamics and its history. It is also a valuable and human account of the Parisian mathematical community in the early-to-middle 20th Century ... . It is amply illustrated with drawings from many of the works cited and photographs of most of the mathematicians mentioned. ... The prose is lively, and the book is very readable." (Daniel S. Alexander, Historia Mathematica, Vol. 41, 2014)

"This is a systematically researched and presented piece of work, with meticulous references. The exposition of the mathematics is particularly clear. ... Audin is aiming this book first and foremost at mathematicians, specifically those mathematicians who are interested in the broad area of mathematics covered in the book, namely complex dynamics. ... Audin's book is not only an interesting read but also an important piece of scholarship." (Christopher Hollings, BSHM Bulletin, Vol. 27 (1), 2012)

"Audin draws the portraits, the environment ... and does it with her own views, her feelings, and her passion for mathematics and for the truth. ... Even specialists in the field will find something new in the book, and nonspecialists will have an excellent introduction to modern complex dynamics. ... For many readers, as for myself, the fact that the author is present on every page with a remark, a comment, and sometimes a mockery, will make it more pleasant and easy to read." (Jean-Pierre Kahane, The Mathematical Intelligencer, Vol. 33 (3), September, 2011)

From the book reviews:“Book is a most welcome addition to the conversation involving complex dynamics and its history. It is also a valuable and human account of the Parisian mathematical community in the early-to-middle 20th Century … . It is amply illustrated with drawings from many of the works cited and photographs of most of the mathematicians mentioned. … The prose is lively, and the book is very readable.” (Daniel S. Alexander, Historia Mathematica, Vol. 41, 2014)“This is a systematically researched and presented piece of work, with meticulous references. The exposition of the mathematics is particularly clear. … Audin is aiming this book first and foremost at mathematicians, specifically those mathematicians who are interested in the broad area of mathematics covered in the book, namely complex dynamics. … Audin’s book is not only an interesting read but also an important piece of scholarship.” (Christopher Hollings, BSHM Bulletin, Vol. 27 (1), 2012)“Audin draws the portraits, the environment … and does it with her own views, her feelings, and her passion for mathematics and for the truth. … Even specialists in the field will find something new in the book, and nonspecialists will have an excellent introduction to modern complex dynamics. … For many readers, as for myself, the fact that the author is present on every page with a remark, a comment, and sometimes a mockery, will make it more pleasant and easy to read.” (Jean-Pierre Kahane, The Mathematical Intelligencer, Vol. 33 (3), September, 2011)