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Tr. Mosk. Mat. Obs., 1963, Volume 12, Pages 3–52 (Mi mmo137)  

This article is cited in 33 scientific papers (total in 34 papers)

On the stability of a center for time-periodic perturbations

V. K. Mel'nikov


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Received: 05.02.1961

Citation: V. K. Mel'nikov, “On the stability of a center for time-periodic perturbations”, Tr. Mosk. Mat. Obs., 12, 1963, 3–52

Citation in format AMSBIB
\Bibitem{Mel63}
\by V.~K.~Mel'nikov
\paper On the stability of a center for time-periodic perturbations
\serial Tr. Mosk. Mat. Obs.
\yr 1963
\vol 12
\pages 3--52
\mathnet{http://mi.mathnet.ru/mmo137}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=156048}
\zmath{https://zbmath.org/?q=an:0135.31001}


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    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. A. D. Bruno, “Instability in a Hamiltonian system and the distribution of asteroids”, Math. USSR-Sb., 12:2 (1970), 271–312  mathnet  crossref  mathscinet  zmath
    2. S. L. Ziglin, “Splitting of the separatrices and the nonexistence of first integrals in systems of differential equations of Hamiltonian type with two degrees of freedom”, Math. USSR-Izv., 31:2 (1988), 407–421  mathnet  crossref  mathscinet  zmath
    3. D. M. Vavriv, V. B. Ryabov, “Running Lyapunov exponents and the conditions for the occurrence of chaos”, Comput. Math. Math. Phys., 32:9 (1992), 1259–1269  mathnet  mathscinet  zmath  isi
    4. V. S. Medvedev, E. L. Fedorov, “On dynamical systems close to Hamiltonian with separatrix loops of a saddle”, Russian Acad. Sci. Sb. Math., 83:1 (1995), 79–91  mathnet  crossref  mathscinet  zmath  isi
    5. V. M. Rotos, “Homoclinic Orbits for a Perturbed Lattice Modified KdV Equation”, Theoret. and Math. Phys., 134:1 (2003), 117–127  mathnet  crossref  crossref  mathscinet  isi
    6. B. R. Andrievsky, A. L. Fradkov, “Control of Chaos: Methods and Applications. I. Methods”, Autom. Remote Control, 64:5 (2003), 673–713  mathnet  crossref  mathscinet  zmath  isi
    7. A. I. Neishtadt, “Capture into Resonance and Scattering on Resonances in Two-Frequency Systems”, Proc. Steklov Inst. Math., 250 (2005), 183–203  mathnet  mathscinet  zmath
    8. K. V. Koshel', S. V. Prants, “Chaotic advection in the ocean”, Phys. Usp., 49:11 (2006), 1151–1178  mathnet  crossref  crossref  adsnasa  isi
    9. A. Yu. Kolesov, E. F. Mishchenko, N. Kh. Rozov, “Buffer phenomenon in systems close to two-dimensional Hamiltonian ones”, Proc. Steklov Inst. Math. (Suppl.), 253, suppl. 1 (2006), S117–S150  mathnet  crossref  mathscinet  zmath  elib
    10. A. Yu. Loskutov, “Dynamical chaos: systems of classical mechanics”, Phys. Usp., 50:9 (2007), 939–964  mathnet  crossref  crossref  adsnasa  isi  elib
    11. M. Bobieński, H. Żołądek, “A counterexample to a multidimensional version of the weakened Hilbert's 16th problem”, Mosc. Math. J., 7:1 (2007), 1–20  mathnet  mathscinet  zmath
    12. N. E. Kulagin, L. M. Lerman, T. G. Shmakova, “Fronts, traveling fronts, and their stability in the generalized Swift–Hohenberg equation”, Comput. Math. Math. Phys., 48:4 (2008), 659–676  mathnet  crossref  mathscinet  zmath  isi
    13. L. A. Kalyakin, “Asymptotic analysis of autoresonance models”, Russian Math. Surveys, 63:5 (2008), 791–857  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    14. V. S. Aslanov, B. V. Ivanov, “Khaoticheskoe dvizhenie nelineinoi sistemy”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 8:4 (2008), 38–43  mathnet
    15. V. N. Tkhai, “On models structurally stable in periodic motion”, Autom. Remote Control, 70:9 (2009), 1584–1589  mathnet  crossref  mathscinet  zmath  isi
    16. R. E. Kondrashov, A. D. Morozov, “K issledovaniyu rezonansov v sisteme dvukh uravnenii Dyuffinga–Van der Polya”, Nelineinaya dinam., 6:2 (2010), 241–254  mathnet  elib
    17. S. A. Korolev, A. D. Morozov, “O periodicheskikh vozmuscheniyakh avtokolebatelnykh mayatnikovykh uravnenii”, Nelineinaya dinam., 6:1 (2010), 79–89  mathnet  elib
    18. Tkhai V.N., “The Period on a Family of Non-Linear Oscillations and Periodic Motions of a Perturbed System at a Critical Point of the Family”, Pmm-J. Appl. Math. Mech., 74:5 (2010), 579–586  crossref  mathscinet  isi
    19. V. N. Tkhai, “Oscillations and stability in quasiautonomous system. II. Critical point of the one-parameter family of periodic motions”, Autom. Remote Control, 72:7 (2011), 1450–1457  mathnet  crossref  mathscinet  zmath  isi
    20. Aslanov V.S., “Kolebaniya sputnika s vertikalnym uprugim trosom na orbite”, Izvestiya rossiiskoi akademii nauk. mekhanika tverdogo tela, 2011, no. 5, 3–15  elib
    21. Makarenkov O., Malaguti L., Nistri P., “On the Behavior of Periodic Solutions of Planar Autonomous Hamiltonian Systems with Multivalued Periodic Perturbations”, Z. Anal. ihre. Anwend., 30:2 (2011), 129–144  crossref  mathscinet  zmath  isi  elib
    22. D. A. Losyakova, “Khaoticheskoe dvizhenie volchka so smeschennym tsentrom mass”, Izv. Sarat. un-ta. Nov. ser. Ser. Matematika. Mekhanika. Informatika, 12:2 (2012), 90–95  mathnet
    23. Aslanov V.S., Ledkov A.S., “Khaoticheskie kolebaniya ka c uprugim radialno orientirovannym trosom”, Kosmicheskie issledovaniya, 50:2 (2012), 194–194  elib
    24. O. M. Kiselev, “Oscillations near a separatrix in the Duffing equation”, Proc. Steklov Inst. Math. (Suppl.), 281, suppl. 1 (2013), 82–94  mathnet  crossref  isi  elib
    25. I. N. Barabanov, V. N. Tkhai, “Quasi-Autonomous Systems: Oscillations, Stability, and Stabilization in the Regular Point of the Family of Periodic Solutions”, Autom. Remote Control, 74:8 (2013), 1257–1268  mathnet  crossref  isi  elib  elib
    26. A. I. Neishtadt, “Averaging, passage through resonances, and capture into resonance in two-frequency systems”, Russian Math. Surveys, 69:5 (2014), 771–843  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib
    27. Amadeu Delshams, Marina Gonchenko, Pere Gutiérrez, “Continuation of the Exponentially Small Transversality for the Splitting of Separatrices to a Whiskered Torus with Silver Ratio”, Regul. Chaotic Dyn., 19:6 (2014), 663–680  mathnet  crossref  mathscinet  zmath
    28. O. G. Bakunin, “Stochastic instability and turbulent transport. Characteristic scales, increments, and diffusion coefficients”, Phys. Usp., 58:3 (2015), 252–285  mathnet  crossref  crossref  adsnasa  isi  elib
    29. Trans. Moscow Math. Soc., 76:2 (2015), 271–299  mathnet  crossref  elib
    30. O. S. Kostromina, “K issledovaniyu bifurkatsionnykh i khaoticheskikh yavlenii v sisteme s gomoklinicheskoi «vosmerkoi»”, Nelineinaya dinam., 12:1 (2016), 31–52  mathnet
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    32. O. G. Bakunin, “Quasilinear theory of plasma turbulence. Origins, ideas, and evolution of the method”, Phys. Usp., 61:1 (2018), 52–83  mathnet  crossref  crossref  adsnasa  isi  elib
    33. N. I. Makarenko, Z. V. Makridin, “Periodic oscillations and waves in nonlinear weakly coupled dispersive systems”, Proc. Steklov Inst. Math., 300 (2018), 149–158  mathnet  crossref  crossref  isi  elib
    34. A. D. Morozov, K. E. Morozov, “On Synchronization of Quasiperiodic Oscillations”, Nelineinaya dinam., 14:3 (2018), 367–376  mathnet  crossref
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