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References:
[1] A. F. Andrejev: Singular points of differential equations. (Russian) Minsk 1979.
[2] A. A. Andronov E. A. Leontovich I. I. Gordon A. G. Mayer: Theory of bifurcations of dynamical systems in the plane. (Russian) Nauka, Moscow 1967.
[3] V. I. Arnold: Lectures on bifurcations in versal families. Russian Mat. Surveys, Uspekhi, 27 (5), (1972), 119-184. MR 0413191
[4] V. I. Arnold: Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields. (Russian) Funk. Anal. Pril., 11 (2), (1977), 1 - 10. MR 0442987
[5] V. I. Arnold: Additional chapters on the theory of ordinary differential equations. (Russian) Nauka, Moscow 1978. MR 0526218
[6] N. N. Bautin E. A. Leontovich: Methods and examples of qualitative study of dynamical systems in the plane. (Russian) Nauka, Moscow 1976. MR 0466732
[7] R. I. Bogdanov: Versal deformations of a singular point of a vector field in the plane in the case of zero eigenvalues. (Russian), Proceedings of the I.G. Petrovski Seminar, 2, (1976), 37-65. MR 0442996
[8] R. I. Bogdanov: Bifurcations of a limit cycle of a family of vector fields in the plane. (Russian), Proceedings of the I. G. Petrovski Seminar, 2, (1976), 23 - 35. MR 0442988
[9] R. I. Bogdanov: Versal deformations of a singular point of vector fields in the plane. (Russian), Funk. Anal. Pril., 13 (1), (1979), 63-64. MR 0527524
[10] T. Bröcker L. Lander: Differentiable germs and catastrophes. Cambridge Univ. Press, Cambridge 1975. MR 0494220
[11] J. Carr: Applications of centre manifold theory. Appl. Math. Sciences 35, Springer-Verlag 1981. DOI 10.1007/978-1-4612-5929-9 | MR 0635782 | Zbl 0464.58001
[12] M. Golubitsky V. Guillemin: Stable mappings and their singularities. Springer-Verlag, New York-Heidelberg-Berlin 1973. MR 0341518
[13] J. Guckenheimer: On a codimension two bifurcation. Dynamical Systems and Turbulence, Proc. Symp., Warwick 1980, Springer Verlag, Berlin-Heidelberg-New York 1981, 99-142. MR 0654886
[14] N. Kopell L. N. Howard: Bifurcations and trajectories joining critical points. Adv. Math. 18(1976), 306-358. MR 0397078
[15] B. Malgrange: Ideals of differentiable functions. Oxford Univ. Press 1966. MR 0212575 | Zbl 0177.17902
[16] J. E. Marsden M. McCrecken: The Hopf bifurcation and its applications. Springer Verlag, New York-Heidelberg-Berlin 1976. MR 0494309
[17] J. E. Marsden: Qualitative methods in bifurcation theory. Bull. Amer. Math. Soc., Vol. 84, No. 6 (1978), 1125-1148. DOI 10.1090/S0002-9904-1978-14549-2 | MR 0508450 | Zbl 0404.35010
[18] J. G. Sinaj L. P. Šilnikov: Strange attractors. Proceedings, (Russian) Mir, Moscow 1981. MR 0624437
[19] F. Takens: Unfoldings of certain singularities of vector fields: Generalized Hopf bifurcation. J. Diff. Eq. 14 (1973), 476-493. DOI 10.1016/0022-0396(73)90062-4 | MR 0339264
[20] F. Takens: Forced oscillations. Notes, Ultrecht 1974.
[21] Yung-Chen Lu: Singularity theory and an introduction to catastrophe theory. Springer Verlag, New York-Heidelberg-Berlin 1976. MR 0461562 | Zbl 0354.58008
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