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Unfoldings of certain singularities of vectorfields: Generalized Hopf bifurcations. (English) Zbl 0273.35009


MSC:

35F20 Nonlinear first-order PDEs
34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
35B99 Qualitative properties of solutions to partial differential equations
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References:

[1] \( \textsc{M. Barbançon}C^r \); \( \textsc{M. Barbançon}C^r \) · Zbl 0253.26010
[2] Hopf, E., Abzweigung einer periodischen Lösung von einer stationairen Lösung eines Differential systems, Ber. Math.-Phys. Kl. Sächs. Akad. Wiss. Leipzig, 94, 1-22 (1942)
[3] Kelley, A., The stable, center-stable, center, center-unstable and unstable manifolds, (Abraham, R.; Robbin, J., Transversal Mappings and Flows (1967), Benjamin: Benjamin New York), Appendix C · Zbl 0173.11001
[4] J. P. Lasalle; J. P. Lasalle
[5] Malgrange, B., Ideals of Differentiable Functions (1966), Oxford Univ. Press: Oxford Univ. Press London · Zbl 0177.17902
[6] Wall, C. T.C., (Proceedings of Liverpool Singularities—Symposium I. Proceedings of Liverpool Singularities—Symposium I, Lecture Notes in Mathematics 192 (1971), Springer: Springer New York/Berlin) · Zbl 0211.00202
[7] Ruelle, D.; Takens, F., Commun. Math. Phys., 23, 343-344 (1971) · Zbl 0227.76084
[8] Takens, F., Normal forms for certain singularities of vectorfields, Ann. Inst. Fourier (Grenoble), 23, 163-195 (1973), (2) · Zbl 0266.34046
[9] F. Takens; F. Takens · Zbl 0237.58012
[10] Thom, T., Stabilité Structurelle et Morphogénèse (1972), Benjamin: Benjamin New York
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