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Bifurcations of invariant manifolds of differential equations and normal forms in neighborhoods of elliptic curves. (English. Russian original) Zbl 0346.58003

Funct. Anal. Appl. 10, 249-259 (1977); translation from Funkts. Anal. Prilozh. 10, No. 4, 1-12 (1976).

MSC:

58C25 Differentiable maps on manifolds
14H20 Singularities of curves, local rings
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References:

[1] A. A. Andronov and E. A. Leontovich, ”Certain cases of the dependence of limit cycles on a parameter,” Uch. Zap. Gor’k. Univ.,3 (1939); Collected Works of A. A. Andronov [in Russian], Izd. Akad. Nauk SSSR (1956), p. 188.
[2] V. I. Arnol’d, ”Remarks on the singularities of root codimension in complex dynamic systems,” Funkts. Anal. Prilozhen.,3, No. 1, 1-6 (1969). · Zbl 0249.34035
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[5] A. D. Bryuno, ”Analytic form of differential equations,” Trudy Mosk. Matem. Obshch.,25, 120-262 (1971). · Zbl 0263.34003
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[7] H. Grauert, ”Über Modifikationen und exzeptionelle analytische Mengen,” Ann. Math.,146, 331-368 (1962). · Zbl 0173.33004
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[9] C. L. Siegel, ”On the integrals of canonical systems,” Ann. Math.,42, 806-822 (1941). · Zbl 0025.26503
[10] H. Poincaré, Thèse (1879); Oeuvres, t. 1, Paris (1928).
[11] A. S. Pyartli, ”Generation of complex invariant manifolds close to a singular point of a vector field depending on a parameter,” Funkts. Anal. Prilozhen.,6, No. 4, 95-96 (1972).
[12] E. Hopf, ”Abzweigung einer periodischen Lösung von einer stationären Losung,” Berich. Sächs. Akad. Wiss., Leipzig, Math. Phys. Kl.,94, No. 19, 15-25 (1942).
[13] A. Ogus, ”The formal Hodge filtration,” Invent. Math.,31, No. 3, 193-228 (1976). · Zbl 0339.14004
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