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E-raamat: Origins of Holomorphic Dynamics: A Historical Study of the Topic Selected for the Grand Prix des Mathematiques (1915-1918)

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Origins of Holomorphic Dynamics: A Historical Study of the Topic Selected for the Grand Prix des Mathematiques (1915-1918)Suurem pilt
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This book offers a historical and analytical study of the origins of holomorphic dynamicsa field linking analytic functions with the behavior of iterated orbits. Central to this account is the 19151918 Grand Prix des Sciences Mathématiques, whose winning manuscript extended local research to the entire Riemann sphere and highlighted the striking properties of boundaries between basins of convergence.



Viewed broadly, this event marked a convergence of research traditions from the eighteenth and nineteenth centuriesinfinitesimal calculus, singular points, infinite series, functional equations, root separation, complex analysis, multi-valued functions, and sequences of functionseach a cornerstone for the general theory that now holds a prominent place in modern analysis.



Drawing on unpublished archival material, original French sources, and the intellectual context of early twentieth-century mathematics, the book reconstructs how scientific ambitions and evolving techniques shaped foundational developments in the analysis of complex functions and their iterative dynamics. Blending historical narrative with critique and technical insight, it will appeal to scholars and students interested in the history of mathematics, holomorphic dynamics, and the interplay between ideas and their historical milieu.
1 Introduction.- 2 Tools of infinity.- 3 Overview of the educational
system.- 4 Parental bonds.- 5 Of functionals, notations, and iterates.- 6
Marvels of function composition.- 7 Now it is complex analysis.- 8 A truly
essential point.- 9 Prodigious theorems.- 10 Multi-valued functions.- 11
Confluence.- 12 We who are not as others.- 13 The inception of holomorphic
dynamics.- 14 On the eastern front.- 15 Assessments.- 16 Gearing up for new
discoveries.- 17 The Grand Prix of 1918.- 18 Epilogue.- 19 Insights and
Fill-ins.- 20 Contributions to complex analysis.- Julias memoir on the
iteration of meromorphic functions.- 21 Remarks on the memoir.- 22 The four
sealed envelopes.- Grand Prix des Mathématiques - Dossier.- 23 Presentation
of the dossier.- 24 The reports.- 25 The manuscript of Salvatore Pincherle.-
Appendices.- A Normal families: an exegesis of Julias and Fatous memoirs.-
B Baires theory.- C A stranger in a strange land.- D Incommensurable avec
2.- References.- Alphabetical Index.
Alessandro Rosa is a freelance researcher in the history of mathematics, and co-author of the book "Early Days in Complex Dynamics: A History of Complex Dynamics in One Variable During 1906-1942", co-published by the AMS and the London Mathematical Society in 2011.
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