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About the cover: The fine-Petrović polygons and the Newton-Puiseux method for algebraic ordinary differential equations. (English) Zbl 1443.34002


MSC:

34-03 History of ordinary differential equations
01A55 History of mathematics in the 19th century
34A25 Analytical theory of ordinary differential equations: series, transformations, transforms, operational calculus, etc.
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[2] Bruno, A. D.; Goryuchkina, I. V., Asymptotic expansions of solutions of the sixth Painlev\'{e} equation, Tr. Mosk. Mat. Obs.. Trans. Moscow Math. Soc., 71, 1-104 (2010) · Zbl 1215.34113 · doi:10.1090/S0077-1554-2010-00186-0
[3] Cano, Jos\'{e}, An extension of the Newton-Puiseux polygon construction to give solutions of Pfaffian forms, Ann. Inst. Fourier (Grenoble), 43, 1, 125-142 (1993) · Zbl 0766.34006
[4] Cano, Jos\'{e}, On the series defined by differential equations, with an extension of the Puiseux polygon construction to these equations, Analysis, 13, 1-2, 103-119 (1993) · Zbl 0793.34009 · doi:10.1524/anly.1993.13.12.103
[5] ConnrRobertson J.J.O’Connor and E.F.Robertson “Henry Burchard Fine”, MacTutor History of Mathematics archive, University of St Andrews, 2005.
[6] Dra2019 V. Dragovi\'c, “Mihailo Petrovi\'c, algebraic geometry and differential equations”, in Stevan Pilipovi\'c, Gradimir V. Milovanovi\'c, \v Zarko Mijajlovi\'c (editors), Mihailo Petrovi\'c Alas: life work, times, Serbian Academy of Sciences and Arts, Belgrade, 2019.
[7] DG2019 V. Dragovi\'c and I. Goryuchkina, Polygons of Petrovi\'c and Fine, algebraic ODEs, and contemporary mathematics, Arch. Hist. Exact Sci. (to appear). arXiv:1908.03644 (2019). · Zbl 1471.01016
[8] Fine, Henry B., On the functions defined by differential equations, with an extension of the Puiseux polygon construction to these equations, Amer. J. Math., 11, 4, 317-328 (1889) · JFM 21.0302.01 · doi:10.2307/2369347
[9] Fine, Henry B., Singular solutions of ordinary differential equations, Amer. J. Math., 12, 3, 295-322 (1890) · JFM 22.0302.02 · doi:10.2307/2369621
[10] Fuchs L. Fuchs, \"Uber Differentialgleichungen, deren Integrale feste Verzweigungspunkte besitzen, Ges Werke (1885), Vol. II, p.355. · JFM 16.0248.01
[11] Leitch A. Leitch, A Princeton Companion, Princeton University Press, 1978. · Zbl 0603.55007
[12] Petrovich1 M. Petrowitch, Th\`eses: Sur les z\'ero et les infinis des int\'egrales des \'equations diff\'erentielles alg\'ebraiques. Propositions donn\'ees par la Facult\'e, Paris, 1894.
[13] Petrovitch, Michel, Sur une propri\'{e}t\'{e} des \'{e}quations diff\'{e}rentielles int\'{e}grables \`a l’aide des fonctions m\'{e}romorphes doublement p gdriodiques, Acta Math., 22, 1, 379-386 (1899) · JFM 30.0293.01 · doi:10.1007/BF02417881
[14] Pet1a M. Petrovitch, On a property of differential equations integrable using meromorphic double-periodic functions, Theoretical and Applied Mechanics, 45 (2018), no. 1, 121-127. English translation of Petrovitch’s Acta Mathematicae paper, Petrovich2. · Zbl 1474.34612
[15] PetrovicCW Mihailo Petrovi\'c, Collected Works, 15 volumes (Serbian), The State Textbook Company, Belgarde, 1999.
[16] Monografija Stevan Pilipovi\'c, Gradimir V. Milovanovi\'c, \v Zarko Mijajlovi\'c editors, Mihailo Petrovi\'c Alas: life work, times, Serbian Academy of Sciences and Arts, Belgrade, 2019.
[17] Veblen, Oswald, Henry Burchard Fine-In memoriam, Bull. Amer. Math. Soc., 35, 5, 726-730 (1929) · JFM 55.0020.11 · doi:10.1090/S0002-9904-1929-04815-8
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