01.01.02 (Differential equations, dynamical systems, and optimal control)
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Main publications:
R. R. Gontsov, I. V. Goryuchkina, “Convergence of generalized power series solutions of functional equations”, Russian Math. Surveys, 80:3 (2025), 367–425
R. R. Gontsov, I. V. Goryuchkina, “Convergence of formal Dulac series satisfying an algebraic ordinary differential equation”, Sb. Math., 210:9 (2019), 1207–1221
Gontsov R., Goryuchkina I., “An analytic proof of the Malgrange theorem on the convergence of formal solutions of an ODE”, J. Dynam. Control Syst., 22:1 (2016), 91-100
I. V. Goryuchkina, “Classes of finite order formal solutions of an ordinary differential equation”, Chebyshevskii Sb., 17:2 (2016), 64–87
Gontsov R.R., Goryuchkina I.V., “On the convergence of generalized power series satisfying an algebraic ODE”, Asympt. Anal., 93:4 (2015), 311-323
Goryuchkina I.V., “Tochnoe reshenie shestogo uravneniya Penleve i ekzoticheskaya asimptotika”, Doklady AN, 450:4 (2013), 381-383
I. V. Goryuchkina, “Maillet–Malgrange Type Theorem for Generalized Power Series Formally Satisfying an Analytic ODE”, Math. Notes, 119:5 (2026), 874–885
2025
3.
R. R. Gontsov, I. V. Goryuchkina, “Convergence of generalized power series solutions of functional equations”, Russian Math. Surveys, 80:3 (2025), 367–425
2019
4.
R. R. Gontsov, I. V. Goryuchkina, “Convergence of formal Dulac series satisfying an algebraic ordinary differential equation”, Sb. Math., 210:9 (2019), 1207–1221
2016
5.
Gontsov R., Goryuchkina I., “An analytic proof of the Malgrange theorem on the convergence of formal solutions of an ODE”, J. Dynam. Control Syst., 22:1 (2016), 91-100
I. V. Goryuchkina, “Classes of finite order formal solutions of an ordinary differential equation”, Chebyshevskii Sb., 17:2 (2016), 64–87
2015
7.
Gontsov R.R., Goryuchkina I.V., “On the convergence of generalized power series satisfying an algebraic ODE”, Asympt. Anal., 93:4 (2015), 311-323
8.
I. V. Goryuchkina, “Klassy formalnykh reshenii algebraicheskikh ODU, vychislyaemykh metodami ploskoi stepennoi geometrii”, Preprinty IPM im. M. V. Keldysha, 2015, 73, 26 pp.
2014
9.
I. V. Goryuchkina, “On convergence of generalized power series that is a formal solution of algebraic ODE in the general case”, Keldysh Institute preprints, 2014
10.
I. V. Goryuchkina, “On convergence of generalized power series that is the formal solution of algebraic ODE”, Keldysh Institute preprints, 2014
2013
11.
Goryuchkina I.V., “Tochnoe reshenie shestogo uravneniya Penleve i ekzoticheskaya asimptotika”, Doklady AN, 450:4 (2013), 381-383
12.
I. V. Goryuchkina, “On convergence of power series solution with nonrational power exponents of algebraic ODE”, Keldysh Institute preprints, 2013
13.
A. D. Bruno, I. V. Goryuchkina, “Convergence of power expansions of solutions to an ODE”, Keldysh Institute preprints, 2013
2012
14.
I. V. Goryuchkina, “O kratnykh i nekratnykh resheniyakh algebraicheskikh ODU”, Preprinty IPM im. M. V. Keldysha, 2012, 83, 12 pp.
I. V. Goryuchkina, “The Picard solution of the sixth Painlevé equation and asymptotic forms found by Power Geometry.”, Keldysh Institute preprints, 2011
16.
I. V. Goryuchkina, “Theorem on convergence of a formal solution of ODE”, Keldysh Institute preprints, 2011
I. V. Goryuchkina, “Three-dimensional analysis of asymptotic forms of the solutions to the sixth Painlevé equation.”, Keldysh Institute preprints, 2010
2009
19.
A. D. Bruno, I. V. Goryuchkina, “Elliptic asymptotic forms of solutions to the Painlev'e equations”, Keldysh Institute preprints, 2009
20.
A. D. Bruno, I. V. Goryuchkina, “Non-formal solutions to ODE”, Keldysh Institute preprints, 2009
2008
21.
A. D. Bruno, I. V. Goryuchkina, “All expansions of solutions to the sixth Painlevé equation near its nonsingular point”, Keldysh Institute preprints, 2008
2007
22.
A. D. Bruno, I. V. Goryuchkina, “All asymptotic expansions of solutions to the equation P6 are obtained from base ones”, Keldysh Institute preprints, 2007
23.
A. D. Bruno, I. V. Goryuchkina, “All asymptotic expansions of solutions to the equation P6 in the case $a\cdot b=0$”, Keldysh Institute preprints, 2007
24.
A. D. Bruno, I. V. Goryuchkina, “All base asymptotic expansions of solutions to the equation P6 in the case $a\cdot b\ne0$”, Keldysh Institute preprints, 2007
25.
A. D. Bruno, I. V. Goryuchkina, “Methods are used for researching of asymptotic expansions of solutions to the equation P6”, Keldysh Institute preprints, 2007
26.
A. D. Bruno, I. V. Goryuchkina, “Review of all asymptotic expansions of solutions to the equation P6”, Keldysh Institute preprints, 2007
27.
A. D. Bruno, I. V. Goryuchkina, “All asymptotic expansions of solutions to the sixth Painlevé equation”, Keldysh Institute preprints, 2007
28.
I. V. Goryuchkina, “Exotic expansions of solutions to the sixth Painlevé equation”, Keldysh Institute preprints, 2007
2006
29.
A. D. Bruno, I. V. Goryuchkina, “Expansions of solutions to the sixth Painlevé equation near singular points $x=0$ и $x=\infty$”, Keldysh Institute preprints, 2006
30.
A. D. Bruno, I. V. Goryuchkina, “Expansions of solutions to the sixth painleve equation in cases $a=0$ and $b=0$”, Keldysh Institute preprints, 2006
2005
31.
A. D. Bruno, I. V. Goryuchkina, “Power expansions of solutions to the sixth Painlevé equation near a regular point”, Keldysh Institute preprints, 2005
2026
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