Takens, Floris Unfoldings of certain singularities of vectorfields: Generalized Hopf bifurcations. (English) Zbl 0273.35009 J. Differ. Equations 14, 476-493 (1973). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 65 Documents 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 PDFBibTeX XMLCite \textit{F. Takens}, J. Differ. Equations 14, 476--493 (1973; Zbl 0273.35009) Full Text: DOI 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 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.