Full Description
This book offers a historical and analytical study of the origins of holomorphic dynamics—a field linking analytic functions with the behavior of iterated orbits. Central to this account is the 1915-1918 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 centuries—infinitesimal calculus, singular points, infinite series, functional equations, root separation, complex analysis, multi-valued functions, and sequences of functions—each 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Drawing on unpublished archival material, original French sources, and the intellectual context of early twentieth-century mathematics, the book reconstructs how scientific ambitions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.
Contents
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.- Julia's 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 Julia's and Fatou's memoirs.- B Baire's theory.- C A stranger in a strange land.- D Incommensurable avec 2π.- References.- Alphabetical Index.
