LEADER 04038nam 22005535 450 001 9911064734903321 005 20260213121653.0 010 $a3-032-17106-7 024 7 $a10.1007/978-3-032-17106-1 035 $a(CKB)45322514600041 035 $a(MiAaPQ)EBC32549239 035 $a(Au-PeEL)EBL32549239 035 $a(DE-He213)978-3-032-17106-1 035 $a(OCoLC)1574819025 035 $a(EXLCZ)9945322514600041 100 $a20260213d2026 u| 0 101 0 $aeng 135 $aur||||||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 14$aThe Origins of Holomorphic Dynamics $eA Historical Study of the Topic Selected for the Grand Prix des Mathématiques (1915?1918) /$fby Alessandro Rosa 205 $a1st ed. 2026. 210 1$aCham :$cSpringer Nature Switzerland :$cImprint: Birkhäuser,$d2026. 215 $a1 online resource (504 pages) 225 1 $aMathematics and Statistics Series 311 08$a3-032-17105-9 327 $a1 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 2? -- References -- Alphabetical Index. 330 $aThis book offers a historical and analytical study of the origins of holomorphic dynamics?a field linking analytic functions with the behavior of iterated orbits. Central to this account is the 1915?1918 Grand Prix des Sciences Mathématiques, whose winning manuscript extended local research to the entire Riemann sphere and highlighted the striking properties of boundaries between basins of convergence. Viewed broadly, this event marked a convergence of research traditions from the eighteenth and nineteenth centuries?infinitesimal calculus, singular points, infinite series, functional equations, root separation, complex analysis, multi-valued functions, and sequences of functions?each a cornerstone for the general theory that now holds a prominent place in modern analysis. Drawing on unpublished archival material, original French sources, and the intellectual context of early twentieth-century mathematics, the book reconstructs how scientific ambitions and evolving techniques shaped foundational developments in the analysis of complex functions and their iterative dynamics. Blending historical narrative with critique and technical insight, it will appeal to scholars and students interested in the history of mathematics, holomorphic dynamics, and the interplay between ideas and their historical milieu. 410 0$aMathematics and Statistics Series 606 $aMathematics 606 $aHistory 606 $aDynamics 606 $aHistory of Mathematical Sciences 606 $aDynamical Systems 615 0$aMathematics. 615 0$aHistory. 615 0$aDynamics. 615 14$aHistory of Mathematical Sciences. 615 24$aDynamical Systems. 676 $a510.9 700 $aRosa$b Alessandro$0515224 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9911064734903321 996 $aThe Origins of Holomorphic Dynamics$94545742 997 $aUNINA