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Is there any English translation of the 1918-1920 Memoirs of Fatou and Julia on the iteration of rational functions?

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  • $\begingroup$ Rosa translated Julia's Grand Prix memoir, but only opening pages are available online. There are detailed summaries and historical context in Early Days in Complex Dynamics. $\endgroup$
    – Conifold
    Commented Mar 3 at 7:05
  • $\begingroup$ I remember that there was a project of translating Julia papers, and I was even asked to proofread some translations. But I don't know what happened to this project and whether translations were posted on Internet. Concerning Fatou, there are no translations that I know about. I recommended to the authors to translate Fatou, since on my opinion Fatou's papers are much more valuable, but for some reasons they did not want to, and were only interested in Julia. But this was long ago. $\endgroup$ Commented Mar 3 at 13:56
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    $\begingroup$ An analysis and comparison of the work of Fatou and Julia on holomorphic dynamics is contained in the book by Michele Audin "Fatou, Julia, Monetl,,,". It is quite complete, and this book has been translated into English. $\endgroup$ Commented Mar 3 at 13:59
  • $\begingroup$ Now I recall something about the project mentioned in my first remark. The name of translator was Alexandro Rosa, and here is his translation of the first 10 pages of Julia: emis.de/journals/AMEN/posters/poster0171.pdf Apparently the project was abandonned. $\endgroup$ Commented Mar 3 at 14:04
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    $\begingroup$ I posted my response below. Thanks for getting interested. $\endgroup$ Commented Mar 3 at 22:05

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I was pointed to this chain of messages and I would then like giving you my version of facts. The translations project was the very very early version of the contents that ended up in the book I published for AMS in the end of 2011. It started for my personal knowledge and fruition.

I can't recall exactly how the files of Julia's memoir translations spread online, as facts date back to more than twenty years ago. This was not my concern at all in then times as I was aware that the quality was not worth the circulation, and honestly I would have liked them to be removed when I discovered they had been put online (a few years later). Anyway I could not know how to do that, since I could not find out whom to call for. I just have a bare recollection that I shared'em with somebody, for pure show. Things went out of my control.

And yes, professor Eremenko is right: I suspended the work on translations. Or maybe I gave up. But there were some valid motivations: first, due to the above book. Second, at the time I was not sure they might really be of interest for publishers or readers. Most of them are original memoirs or articles, written in French. Which I presumed that most mathematicians, and amateurs, are able to read it. I thought they might have not been of use for anybody- Moreover, I am not a native english speaker, so I was not quite confident in spreading them, since they need revision before being made public.

You would like to know that Julia's are not the only translations I did. I have much more material:almost all Julia's works up to early 1920, including the memoir of 1919-21, where Julia discovered the so-called "lines of Julia", inherent to the neighboring behavior about essential singularities and, as you know, quite close on Julia set. There would be only the memoir about permutable maps to be translated. In addition, there are also almost all Fatou's works on iterations, except the long memoir of 1919-20, the one you mentioned in your messages. That I did not at the time, because of the original plan changed. Again, the translation of the two articles by Samuel Lattès appearing in Comptes Rendus of 1918 (about Julia set filling the Riemann sphere) and the three works by Hubert Cremer, where he explored the dynamics around non-linearizable indifferent points of irrational kind.

The original plan behind the next-to-be aforementioned book consisted in releasing a collection of those early articles that would have covered nearly fifty years of holomorphic dynamics, spanning from Schroder and Koenigs, up to Fatou, Julia and Cremer. Including Bottcher's production: either his thesis of 1899 (compiled in German) and mostly the later production around 1904, which anticipated the discovery of so-called "Fatou-Leau's flower". (By the way, Ernst Lémeray accomploished it too shortly before Leau's thesis). Bottcher went to a thorough analysis of this same question, pretty much interesting on my viewpoint. The original work is in Russian, and I know the contents thanks to a native Polish-Russian speaker who translated some of those pages.

In conclusion, I gave up because I would have liked joining a task force including a native speaker / mathematicians (German for Cremer, Russian for Bottcher at least). Take care that the original format of my files is still MS Word, so they need be turned into LaTeX first.

I am currently busy with the submission of a new history book on holomorphic dynamics, that covers some of the topics I resumed above. But I am open to resume this translations project, if there would be margins of interest. According to the above, it naturally goes that I would be very prone to any form of cooperation and coordination.

Thanks for showing interest. Hope I have fulfilled your curiosities. Feel free to write me to [email protected]

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  • $\begingroup$ Thank you for sharing. I suspect that most English-speaking mathematicians, and especially amateurs, are unable to read French. At least, not well enough to follow complex mathematical arguments. I do not know how realistic it is to find a publisher for your translations, or to assemble a task force, but if it does not work out I hope you will find a way to make them public. Even raw translations in Word, maybe converted into pdf, would make the works accessible to many people who cannot read them today and benefit from the original flow of ideas. Perfect should not be the enemy of good. $\endgroup$
    – Conifold
    Commented Mar 4 at 21:20
  • $\begingroup$ I understand that the amount of pages would be too huge for a printed publication. It would be nice then for some academic istitution to grant some free web space, that I could manage and progressively fill in with translations. My plan would be to turn MS word format into LaTeX and the generate the PDF. I feel more confident with LaTeX nowadays: when I first compiled the translation, I didn't know this tool yet. It's my standard for producing PDF. $\endgroup$ Commented Mar 5 at 7:43
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    $\begingroup$ Did you consider arXiv? It is Latex friendly and automatically generates pdf. Some authors post their translations there, e.g. Aycock and Bistafa. Clicking on the poster's name one can see all of their posts, so all your translations will be gathered in one place. Of course, that makes them freely available, so I am not sure if you want to do that when there is a prospect of publication. $\endgroup$
    – Conifold
    Commented Mar 5 at 8:26
  • $\begingroup$ Thanks for suggesting, but at the moment ArXiV looks too rigid to me. I had troubles with permissions in the past, because I needed someone crediting me, my reputation and my uploads. I would like having an all-in-one solution .... I mean to a web page where I can mantain contents on my own,; lists, downloads, texts by means of a FTP connection. Besides translations, there's some additional material that I would like sharing and that it is not compatible with publishing on ArXiV. $\endgroup$ Commented Mar 5 at 9:35
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    $\begingroup$ Btw, yes, 40+ years ago most professional mathematicians could read English, French, and German, of necessity. This seems no longer true. So, yes, for the future, translations into English are very useful, even if in a kinda-pathetic way. :) $\endgroup$ Commented Mar 15 at 22:37
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Before posting my thoughts I would like to thank everyone for contributing to this inquiry and express my sincere appreciation for Mr Rosa's answer.

I have read parts of two books on the history of complex dynamics

  1. A History of Complex Dynamics From Schröder to Fatou and Julia
  2. Early Days in Complex Dynamics: A history of complex dynamics in one variable during 1906–1942

I have to say it was quite a joy reading through their chapters, and I found them very helpful and informative for a plethora of aspects regarding the theory itself.

Before continuing further though, I need to say that I am not an expert in the field, as I am about to begin my PhD on holomorphic dynamics in autumn this year. So, my knowledge about publishing is minimal at best, if nonexistent. Furthermore, I am neither a native English speaker, nor a French one, but I manage to understand a little bit of the latter.

Last year I completed a Master's Thesis on the subject, but there were no faculty members in my university studying complex dynamics, (my thesis committee was comprised of some external experts on complex dynamics though). Therefore, I had to learn the theory on my own, and at the time, I was finding the books available a little difficult to crack through their line of thought and motivation behind some concepts, especially the first time I encountered some ideas. This was the case with the Leau-Fatou theorem for example, where on the other hand Fatou's original Memoir provided much needed (for me) explanation and details.

Furthermore, it strikes me, how much these men understood the subject they were studying. One can find evidence for that on pages 158 to 170 of Julia's online available Memoir, for example. Of course, nowadays with the help of computers, we can easily visualize Julia sets, but I find the thought that Fatou and Julia suspected the complexity of the objects they were dealing with quite appealing.

In my opinion, these Memoirs could serve as an auxiliary introduction for the subject and translating them into English could help popularize the field and help lower the "entry barrier" for students, as both Fatou's and Julia's Memoirs contain many worked-out and very detailed examples, something that many of the books I encountered partially lack, and provide strong motivation for many concepts now standardized in the theory. Moreover, I agree with Mr Rosa's remark that comments and graphics would constitute a great enhancement.

I understand Mr Rosa's objections to making the translated documents public, but as Conifold pointed out, "Even raw translations in Word, maybe converted into pdf, would make the works accessible to many people who cannot read them today and benefit from the original flow of ideas", and I have experienced this benefiting myself.

In conclusion, I believe that such a collection of translated documents could greatly enhance the learning experience, and the study of foundational ideas, and could significantly contribute to the historical aspect of the field. I was puzzled when I began studying complex dynamics and I could not locate a translation of such influential publications, they remind me of Klein's work on the Icosahedron or the Fricke-Klein books.

I would be very pleased if I could be of any help in such a project.

I would like to see your thoughts on those points as naive as they may seem from someone who does not have significant experience with such matters.

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  • $\begingroup$ Thanks for appreciating those two books. Actually, the first entry was instructive for me as well, and was the first reason why I got in touch with the author, Daniel S. Alexander, and we started long and efficacious conversations, which eventually turned into the co-authoring of the second entry. Please, read my post below. $\endgroup$ Commented Mar 5 at 13:07
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This is a longer comment rather than an answer to the question specifically about Fatou and Julia papers. Having been given green light by Sandro, let me add some more details about his project of "releasing a collection of those early articles that would have covered nearly fifty years of holomorphic dynamics, spanning from Schroder and Koenigs, up to Fatou, Julia and Cremer". Sandro and I exchanged emails in 2013-2014 concerning my joint work with Stanislaw Domoradzki on the life and achievements of Lucjan Emil Boettcher. In one such exchange I learned about Sandro's project described in his answer above. Wishing to contribute, I translated (from Polish to English) Boettcher's 1898 article in several parts: ``Zasady rachunku iteracyjnego" [Principles of iterational calculus , Prace Matematyczno Fizyczne, vol. X (1899 1900), pp. 65-86, 86-101, v. XII(1901), p. 95-111, v. XIII(1902), pp. 353-371.

This paper contains most of Boettcher's pioneering ideas in holomorphic dynamics. His 1904 memoir in Russian largely overlaps with it. My translation is almost complete, except typesetting of some elaborate but repetitive formulas in Part III. I feel confident about its accuracy (I am a PhD mathematician, a native speaker of Polish, and I have been living for nearly half of my life in the USA). Sandro helped me with reproducing Boettcher's graphics. This translation could be viewed as a part of his project. It was never published or posted online, because I had no idea what would be a good venue for it (posting on ArXiv not as an author of the contents is tricky, and I do not have a Web page). And (as Sandro already said) there was little external interest. While I do not mind sharing the files, a word of warning is in order. Boettcher's works should be appreciated for the wealth of the ideas they contain, but they suffer from lack of rigor. I pointed this out on many occassions, e.g. here.

Failures in math

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  • $\begingroup$ Margaret, thanks for getting in. I am confident that a good project is starting to come up and develop, thanks to different contributors. I am trying to arrange things to go that way. At this point, old opinions that I may have reasonably held twenty years ago would be senseless nowadays. $\endgroup$ Commented Mar 7 at 10:01
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I will embark on the translation of Fatou's memoir and hopefully get it done by the start of next summer. I am quite confident of it, thanks to the recent re-study for a new book project.

Take care that one such project would be of interest for experts and beginners; hence it's not just about pasting my rough translations into a PDF and share it. Syntax, language, appearance must be worked out.

To Prelude, I posted my email address in the first comment at the top. Write me, in order to check whether we can meet on some point.

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  • $\begingroup$ Sandro, I added an answer about Boettcher's translation being available, as promised. $\endgroup$ Commented Mar 7 at 2:34

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