Gontsov, R. R.; Goryuchkina, I. V. On the convergence of formal exotic series solutions of an ODE. (English) Zbl 1448.34159 Comput. Methods Funct. Theory 20, No. 2, 279-295 (2020). Reviewer: Mykola Grygorenko (Kyïv) MSC: 34M04 34M25 47N20 PDFBibTeX XMLCite \textit{R. R. Gontsov} and \textit{I. V. Goryuchkina}, Comput. Methods Funct. Theory 20, No. 2, 279--295 (2020; Zbl 1448.34159) Full Text: DOI
Dragovic, Vladimir; Gontsov, Renat; Goryuchkina, Irina From formal to actual Puiseux series solutions of algebraic differential equations of first order. arXiv:2008.02982 Preprint, arXiv:2008.02982 [math.CA] (2020). MSC: 34M25 34M04 34M35 BibTeX Cite \textit{V. Dragovic} et al., ``From formal to actual Puiseux series solutions of algebraic differential equations of first order'', Preprint, arXiv:2008.02982 [math.CA] (2020) Full Text: arXiv OA License
Gontsov, Renat R.; Goryuchkina, Irina V. Convergence of formal Dulac series satisfying an algebraic ordinary differential equation. (English. Russian original) Zbl 1435.34091 Sb. Math. 210, No. 9, 1207-1221 (2019); translation from Mat. Sb. 210, No. 9, 3-18 (2019). Reviewer: Dmitry Sinelshchikov (Moskva) MSC: 34M25 34M45 PDFBibTeX XMLCite \textit{R. R. Gontsov} and \textit{I. V. Goryuchkina}, Sb. Math. 210, No. 9, 1207--1221 (2019; Zbl 1435.34091); translation from Mat. Sb. 210, No. 9, 3--18 (2019) Full Text: DOI
Gontsov, Renat; Goryuchkina, Irina The Maillet-Malgrange type theorem for generalized power series. (English) Zbl 1395.34088 Manuscr. Math. 156, No. 1-2, 171-185 (2018). Reviewer: Shun Shimomura (Yokohama) MSC: 34M25 34M30 PDFBibTeX XMLCite \textit{R. Gontsov} and \textit{I. Goryuchkina}, Manuscr. Math. 156, No. 1--2, 171--185 (2018; Zbl 1395.34088) Full Text: DOI arXiv
Gontsov, Renat R.; Goryuchkina, Irina V. Towards the convergence of generalized power series solutions of algebraic ODEs. (English) Zbl 1404.34102 Filipuk, Galina (ed.) et al., Analytic, algebraic and geometric aspects of differential equations. Bȩdlewo, Poland, September 6–19, 2015. Cham: Birkhäuser/Springer (ISBN 978-3-319-52841-0/hbk; 978-3-319-52842-7/ebook). Trends in Mathematics, 325-335 (2017). MSC: 34M25 34A25 PDFBibTeX XMLCite \textit{R. R. Gontsov} and \textit{I. V. Goryuchkina}, in: Analytic, algebraic and geometric aspects of differential equations. Będlewo, Poland, September 6--19, 2015. Cham: Birkhäuser/Springer. 325--335 (2017; Zbl 1404.34102) Full Text: DOI
Goryuchkina, I. V. Classes of finite order formal solutions of an ordinary differential equation. (Russian. English summary) Zbl 1441.34093 Chebyshevskiĭ Sb. 17, No. 2(58), 64-87 (2016). MSC: 34M25 34M55 PDFBibTeX XMLCite \textit{I. V. Goryuchkina}, Chebyshevskiĭ Sb. 17, No. 2(58), 64--87 (2016; Zbl 1441.34093) Full Text: MNR
Gontsov, Renat; Goryuchkina, Irina An analytic proof of the Malgrange theorem on the convergence of formal solutions of an ODE. (English) Zbl 1335.34142 J. Dyn. Control Syst. 22, No. 1, 91-100 (2016). Reviewer: Vladimir P. Kostov (Nice) MSC: 34M25 PDFBibTeX XMLCite \textit{R. Gontsov} and \textit{I. Goryuchkina}, J. Dyn. Control Syst. 22, No. 1, 91--100 (2016; Zbl 1335.34142) Full Text: DOI
Gontsov, R. R.; Goryuchkina, I. V. On the convergence of generalized power series satisfying an algebraic ODE. (English) Zbl 1327.34014 Asymptotic Anal. 93, No. 4, 311-325 (2015). MSC: 34A25 34M25 PDFBibTeX XMLCite \textit{R. R. Gontsov} and \textit{I. V. Goryuchkina}, Asymptotic Anal. 93, No. 4, 311--325 (2015; Zbl 1327.34014) Full Text: DOI arXiv
Goryuchkina, I. V. Exact solution of the sixth Painlevé equation and exotic asymptotic expansion. (English. Russian original) Zbl 1282.34097 Dokl. Math. 87, No. 3, 314-317 (2013); translation from Dokl. Akad. Nauk. 450, No. 4, 381-384 (2013). Reviewer: Dmitri Artamonov (Moscow) MSC: 34M55 34M25 34M30 PDFBibTeX XMLCite \textit{I. V. Goryuchkina}, Dokl. Math. 87, No. 3, 314--317 (2013; Zbl 1282.34097); translation from Dokl. Akad. Nauk. 450, No. 4, 381--384 (2013) Full Text: DOI
Goryuchkina, Irina V. Asymptotic expansions and forms of solutions to \(P_6\). (English) Zbl 1291.34154 Bruno, Alexander D. (ed.) et al., Painlevé equations and related topics. Proceedings of the international conference, Saint Petersburg, Russia, June 17–23, 2011. Berlin: de Gruyter (ISBN 978-3-11-027558-2/hbk; 978-3-11-027566-7/ebook). De Gruyter Proceedings in Mathematics, 27-31 (2012). MSC: 34M55 34E05 34A25 34M30 PDFBibTeX XMLCite \textit{I. V. Goryuchkina}, in: Painlevé equations and related topics. Proceedings of the international conference, Saint Petersburg, Russia, June 17--23, 2011. Berlin: de Gruyter. 27--31 (2012; Zbl 1291.34154)
Bruno, A. D.; Goryuchkina, I. V. Asymptotic expansions of solutions of the sixth Painlevé equation. (English. Russian original) Zbl 1215.34113 Trans. Mosc. Math. Soc. 2010, 1-104 (2010); translation from Tr. Mosk. Mat. O.-va. 71, 6-118 (2010). MSC: 34M55 34M35 34M30 PDFBibTeX XMLCite \textit{A. D. Bruno} and \textit{I. V. Goryuchkina}, Trans. Mosc. Math. Soc. 2010, 1--104 (2010; Zbl 1215.34113); translation from Tr. Mosk. Mat. O.-va. 71, 6--118 (2010) Full Text: DOI
Goryuchkina, I. V. Basic asymptotic expansions of solutions to the sixth Painlevé equation. (English. Russian original) Zbl 1196.34114 J. Math. Sci., New York 160, No. 1, 1-9 (2009); translation from Sovrem. Mat. Prilozh. 57 (2008). Reviewer: John Schmeelk (Doha) MSC: 34M55 34M35 PDFBibTeX XMLCite \textit{I. V. Goryuchkina}, J. Math. Sci., New York 160, No. 1, 1--9 (2009; Zbl 1196.34114); translation from Sovrem. Mat. Prilozh. 57 (2008) Full Text: DOI
Bruno, A. D.; Goryuchkina, I. V. All expansions of solutions to the sixth Painlevé equation near its nonsingular point. (English. Russian original) Zbl 1181.34097 Dokl. Math. 79, No. 3, 397-402 (2009); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 426, No. 5, 586-591 (2009). MSC: 34M55 PDFBibTeX XMLCite \textit{A. D. Bruno} and \textit{I. V. Goryuchkina}, Dokl. Math. 79, No. 3, 397--402 (2009; Zbl 1181.34097); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 426, No. 5, 586--591 (2009) Full Text: DOI
Bruno, A. D.; Goryuchkina, I. V. Basic expansions of solutions to the sixth Painlevé equation in the generic case. (English. Russian original) Zbl 1185.34137 Differ. Equ. 45, No. 1, 18-32 (2009); translation from Differ. Uravn. 45, No. 1, 19-33 (2009). Reviewer: Galina Filipuk (Warszawa) MSC: 34M55 PDFBibTeX XMLCite \textit{A. D. Bruno} and \textit{I. V. Goryuchkina}, Differ. Equ. 45, No. 1, 18--32 (2009; Zbl 1185.34137); translation from Differ. Uravn. 45, No. 1, 19--33 (2009) Full Text: DOI
Bruno, A. D.; Goryuchkina, I. V. Asymptotic forms of solutions to the fourth Painlevé equation. (English. Russian original) Zbl 1221.34238 Dokl. Math. 78, No. 3, 868-873 (2008); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 423, No. 4, 443-448 (2008). MSC: 34M55 34A25 34M30 PDFBibTeX XMLCite \textit{A. D. Bruno} and \textit{I. V. Goryuchkina}, Dokl. Math. 78, No. 3, 868--873 (2008; Zbl 1221.34238); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 423, No. 4, 443--448 (2008) Full Text: DOI
Bruno, A. D.; Goryuchkina, I. V. Asymptotic forms of solutions to the third Painlevé equation. (English. Russian original) Zbl 1193.34175 Dokl. Math. 78, No. 2, 765-768 (2008); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 422, No. 6, 729-732 (2008). Reviewer: Klaus R. Schneider (Berlin) MSC: 34M55 34E05 PDFBibTeX XMLCite \textit{A. D. Bruno} and \textit{I. V. Goryuchkina}, Dokl. Math. 78, No. 2, 765--768 (2008; Zbl 1193.34175); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 422, No. 6, 729--732 (2008) Full Text: DOI
Bruno, A. D.; Goryuchkina, I. V. All asymptotic expansions of solutions to the sixth Painlevé equation. (English. Russian original) Zbl 1158.34347 Dokl. Math. 76, No. 3, 851-855 (2007); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 417, No. 3, 298-302 (2007). MSC: 34M55 34M25 34M30 PDFBibTeX XMLCite \textit{A. D. Bruno} and \textit{I. V. Goryuchkina}, Dokl. Math. 76, No. 3, 851--855 (2007; Zbl 1158.34347); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 417, No. 3, 298--302 (2007) Full Text: DOI
Bruno, A. D.; Goryuchkina, I. V. Expansions of solutions to the sixth Painlevé equation in the cases \(a= 0\) and \(b = 0\). (English. Russian original) Zbl 1160.34077 Dokl. Math. 74, No. 2, 660-665 (2006); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 410, No. 3, 295-300 (2006). Reviewer: Klaus R. Schneider (Berlin) MSC: 34M55 34A25 PDFBibTeX XMLCite \textit{A. D. Bruno} and \textit{I. V. Goryuchkina}, Dokl. Math. 74, No. 2, 660--665 (2006; Zbl 1160.34077); translation from Dokl. Akad. Nauk., Ross. Akad. Nauk. 410, No. 3, 295--300 (2006) Full Text: DOI
Bryuno, A. D.; Goryuchkina, I. V. Expansions of solutions to the sixth Painlevé equation. (English. Russian original) Zbl 1282.34058 Dokl. Math. 69, No. 2, 268-272 (2004); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 395, No. 6, 733-737 (2004). MSC: 34E05 34M55 PDFBibTeX XMLCite \textit{A. D. Bryuno} and \textit{I. V. Goryuchkina}, Dokl. Math. 69, No. 2, 268--272 (2004; Zbl 1282.34058); translation from Dokl. Akad. Nauk, Ross. Akad. Nauk 395, No. 6, 733--737 (2004)