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).


58C25 Differentiable maps on manifolds
14H20 Singularities of curves, local rings
Full Text: DOI


[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
[3] V. I. Arnol’d, ”Singularities of smooth mappings,” Usp. Mat. Nauk,23, No. 1, 3-44 (1968).
[4] V. I. Arnol’d, ”On the mappings of a circumference onto itself,” Izv. Akad. Nauk SSSR, Ser. Matem.,25, No. 1, 21-86 (1961).
[5] A. D. Bryuno, ”Analytic form of differential equations,” Trudy Mosk. Matem. Obshch.,25, 120-262 (1971). · Zbl 0263.34003
[6] A. D. Bryuno, ”Normal form of differential equations with a small parameter,” Matem. Zametki,16, No. 3, 407-414 (1974).
[7] H. Grauert, ”Über Modifikationen und exzeptionelle analytische Mengen,” Ann. Math.,146, 331-368 (1962). · Zbl 0173.33004
[8] C. L. Siegel, ”Iteration of analytic functions,” Ann. Math.,43, 607-612 (1942). · Zbl 0061.14904
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.