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Trudy Matematicheskogo Instituta imeni V.A. Steklova, 2006, Volume 254, Pages 11–100 (Mi tm102)  
This article is cited in 23 scientific papers (total in 23 papers)

On the Analytic Solvability of the Problem of Distinguishing between Center and Focus

N. B. Medvedeva

Chelyabinsk State University
Full-text PDF (873 kB) Citations (23)
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Abstract: The analytic solvability of the problem of distinguishing between a center and a focus is proved in each of semialgebraic subsets whose union is the entire set of monodromic germs.
Received in October 2005
English version:
Proceedings of the Steklov Institute of Mathematics, 2006, Volume 254, Pages 7–93
DOI: https://doi.org/10.1134/S0081543806030023
Bibliographic databases:
UDC: 517.9
Language: Russian
Citation: N. B. Medvedeva, “On the Analytic Solvability of the Problem of Distinguishing between Center and Focus”, Nonlinear analytic differential equations, Collected papers, Trudy Mat. Inst. Steklova, 254, Nauka, MAIK «Nauka/Inteperiodika», M., 2006, 11–100; Proc. Steklov Inst. Math., 254 (2006), 7–93
Citation in format AMSBIB
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\by N.~B.~Medvedeva
\paper On the Analytic Solvability of the Problem of Distinguishing between Center and Focus
\inbook Nonlinear analytic differential equations
\bookinfo Collected papers
\serial Trudy Mat. Inst. Steklova
\yr 2006
\vol 254
\pages 11--100
\publ Nauka, MAIK «Nauka/Inteperiodika»
\publaddr M.
\mathnet{http://mi.mathnet.ru/tm102}
\mathscinet{http://mathscinet.ams.org/mathscinet-getitem?mr=2300999}
\zmath{https://zbmath.org/?q=an:1351.37085}
\elib{https://elibrary.ru/item.asp?id=13523970}
\transl
\jour Proc. Steklov Inst. Math.
\yr 2006
\vol 254
\pages 7--93
\crossref{https://doi.org/10.1134/S0081543806030023}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33749391896}
Linking options:
  • https://www.mathnet.ru/eng/tm102
  • https://www.mathnet.ru/eng/tm/v254/p11
    • This publication is cited in the following 23 articles:
    1. Isaac A. García, Jaume Giné, Ana Livia Rodero, “Dulac functions and monodromic singularities”, Journal of Mathematical Analysis and Applications, 547:2 (2025), 129309  crossref
    2. Isaac A. García, Jaume Giné, Ana Livia Rodero, “Existence and nonexistence of Puiseux inverse integrating factors in analytic monodromic singularities”, Stud Appl Math, 2024  crossref
    3. Isaac A. García, Jaume Giné, “The Poincaré map of degenerate monodromic singularities with Puiseux inverse integrating factor”, Advances in Nonlinear Analysis, 12:1 (2023)  crossref
    4. D. N. Cherginets, “System without Characteristic Directions with a Nonanalytic Center Condition”, Diff Equat, 59:12 (2023), 1598  crossref
    5. Algaba A., Diaz M., Garcia C., Gine J., “Center Problem For Generic Degenerate Vector Fields”, Nonlinear Anal.-Theory Methods Appl., 214 (2022), 112597  crossref  mathscinet  isi  scopus
    6. E. Yu. Liskina, “Dostatochnye usloviya suschestvovaniya tsentra u nelineinoi dinamicheskoi sistemy vtorogo poryadka v odnom kriticheskom sluchae”, Algebra, geometriya, differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 217, VINITI RAN, M., 2022, 51–62  mathnet  crossref
    7. Isaac A. García, Jaume Giné, “Center problem with characteristic directions and inverse integrating factors”, Communications in Nonlinear Science and Numerical Simulation, 108 (2022), 106276  crossref
    8. V. T. Borukhov, “Algebraic Criterion for the Existence of a Center at a Monodromic Singular Point of a Polynomial Liénard System”, Diff Equat, 58:8 (2022), 1008  crossref
    9. N. B. Medvedeva, “Approximate calculation of the coefficients of the Dulac series”, Russian Math. (Iz. VUZ), 65:10 (2021), 31–43  mathnet  crossref  crossref
    10. N. B. Medvedeva, “The problem of distinguishing between a centre and a focus in the space of vector fields with given Newton diagram”, Sb. Math., 211:10 (2020), 1399–1446  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    11. N. B. Medvedeva, V. A. Viktorova, “Granitsa ustoichivosti v odnom prostom klasse monodromnykh rostkov”, Chelyab. fiz.-matem. zhurn., 4:3 (2019), 276–284  mathnet  crossref
    12. N. B. Medvedeva, V. A. Viktorova, “Priblizhennoe vychislenie integralov Adamara spetsialnogo vida”, Chelyab. fiz.-matem. zhurn., 4:4 (2019), 398–411  mathnet  crossref  elib
    13. N. B. Medvedeva, M. A. Sosnovskaya, “Vychislenie koeffitsientov stepennogo ryada preobrazovaniya monodromii v sisteme Maple”, Chelyab. fiz.-matem. zhurn., 2:2 (2017), 181–192  mathnet  mathscinet  elib
    14. N. B. Medvedeva, “Asimptoticheskoe razlozhenie preobrazovaniya monodromii”, Chelyab. fiz.-matem. zhurn., 1:1 (2016), 59–72  mathnet  elib
    15. Korkut L., Vlah D., Zupanovic V., “Geometrical Properties of Systems With Spiral Trajectories in R-3”, Electron. J. Differ. Equ., 2015, 276  mathscinet  zmath  isi
    16. A. S. Voronin, N. B. Medvedeva, “Asymptotics of the monodromy transformation in certain classes of monodromy germs”, Izv. Math., 77:2 (2013), 253–270  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    17. N. B. Medvedeva, “On analytic insolubility of the stability problem on the plane”, Russian Math. Surveys, 68:5 (2013), 923–949  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    18. Gine J., Llibre J., “On the Center Conditions for Analytic Monodromic Degenerate Singularities”, Int. J. Bifurcation Chaos, 22:12 (2012), 1250303  crossref  mathscinet  zmath  isi  elib  scopus
    19. Giné J., “On the degenerate center problem”, Internat. J. Bifur. Chaos Appl. Sci. Engrg., 21:5 (2011), 1383–1392  crossref  mathscinet  zmath  isi  scopus
    20. Voronin A.S., Medvedeva N.B., “Asimptotika preobrazovaniya monodromii v sluchae dvukh chetnykh reber diagrammy nyutona”, Vestnik Chelyabinskogo gosudarstvennogo universiteta, 2011, no. 27, 12–26  elib
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    		Труды Математического института имени В. А. Стеклова Proceedings of the Steklov Institute of Mathematics
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