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JOURNALS // Trudy Instituta Matematiki i Mekhaniki UrO RAN

Trudy Inst. Mat. i Mekh. UrO RAN, 2012, Volume 18, Number 2, Pages 141–153 (Mi timm815)

Oscillations near a separatrix in the Duffing equation
O. M. Kiselev

References

1. Poincare H., Lés méthodes nouvelles de la mécanique célèste, v. III, Gauthier-Villars, Paris, 1892  zmath  adsnasa
2. Melnikov V. K., “On the stability of the center for time periodic perturbations”, Trans. Moscow Math. Soc., 12 (1963), 1–57  mathnet  mathscinet
3. Alekseev V. M., “Kvazisluchainye dinamicheskie sistemy. I”, Mat. sb., 76(118):1 (1968), 72–134  mathnet  mathscinet  zmath; “Квазислучайные динамические системы. II”, Мат. сб., 77(119):4 (1968), 545–601  mathnet  mathscinet  zmath; “Квазислучайные динамические системы. III”, Мат. сб., 78(120):1 (1969), 3–50  mathnet  mathscinet  zmath
4. Filonenko N. N., Sagdeev R. Z., Zaslavskii G. M., “Destruction of magnetic surfaces by magnetic field irregularities. Part II”, Nuclear Fussion, 7 (1967), 253–266  crossref
5. Piftankin G. N., Treschëv D. V., “Separatrisnoe otobrazhenie v gamiltonovykh sistemakh”, Uspekhi mat. nauk, 62:2 (2007), 3–108  mathnet  crossref  mathscinet  zmath  elib
6. Neishtadt A. I., “Passage trough a separatrix in a resonance problem with a slowly-varying parameter”, J. Appl. Math. Mech., 39:4 (1975), 594–605  crossref  mathscinet
7. Timofeev A. V., “On the constancy of an adiabatic invariant when the nature of motion changes”, Soviet Physics JEPT, 48 (1978), 656–659  adsnasa
8. Cary J. R., Scodje R. T., “Phase change between separatrix crossing”, Physica D, 36:3 (1989), 287–316  crossref  mathscinet  zmath  adsnasa  isi
9. Neishtadt A., Vasiliev A., “Phase change between separatrix crossings in slow-fast Hamiltonian systems”, Nonlinearity, 18:3 (2005), 1393–1406  crossref  mathscinet  zmath  adsnasa  isi
10. Diminnie D. C., Haberman R., “Slow passage through a saddle-center bifurcation”, J. Nonlinear Sci., 10:2 (2000), 197–221  crossref  mathscinet  zmath  adsnasa  isi
11. Kiselev O. M., “Hard loss of stability in Painleve-2 equation”, J. Nonlinear Math. Phys., 8:1 (2001), 65–95  crossref  mathscinet  zmath  adsnasa  isi
12. Kiselev O. M., Glebov S. G., “An asymptotic solution slowly crossing the separatrix near a saddle-centre bifurcation point”, Nonlinearity, 16:1 (2003), 327–362  crossref  mathscinet  zmath  adsnasa  isi
13. Ilin A. M., Soglasovanie asimptoticheskikh razlozhenii reshenii kraevykh zadach, Nauka, M., 1989, 336 pp.  mathscinet


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