| Title:
|
The unfoldings of a germ of vector fields in the plane with a singularity of codimension 3 (English) |
| Author:
|
Medveď, Milan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
35 |
| Issue:
|
1 |
| Year:
|
1985 |
| Pages:
|
1-42 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
58C27 |
| MSC:
|
58F14 |
| idZBL:
|
Zbl 0591.58022 |
| idMR:
|
MR779333 |
| DOI:
|
10.21136/CMJ.1985.101994 |
| . |
| Date available:
|
2008-06-09T15:03:16Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101994 |
| . |
| Reference:
|
[1] A. F. Andrejev: Singular points of differential equations.(Russian) Minsk 1979. |
| Reference:
|
[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. |
| Reference:
|
[3] V. I. Arnold: Lectures on bifurcations in versal families.Russian Mat. Surveys, Uspekhi, 27 (5), (1972), 119-184. MR 0413191 |
| Reference:
|
[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 |
| Reference:
|
[5] V. I. Arnold: Additional chapters on the theory of ordinary differential equations.(Russian) Nauka, Moscow 1978. MR 0526218 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[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 |
| Reference:
|
[10] T. Bröcker L. Lander: Differentiable germs and catastrophes.Cambridge Univ. Press, Cambridge 1975. MR 0494220 |
| Reference:
|
[11] J. Carr: Applications of centre manifold theory.Appl. Math. Sciences 35, Springer-Verlag 1981. Zbl 0464.58001, MR 0635782, 10.1007/978-1-4612-5929-9 |
| Reference:
|
[12] M. Golubitsky V. Guillemin: Stable mappings and their singularities.Springer-Verlag, New York-Heidelberg-Berlin 1973. MR 0341518 |
| Reference:
|
[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 |
| Reference:
|
[14] N. Kopell L. N. Howard: Bifurcations and trajectories joining critical points.Adv. Math. 18(1976), 306-358. MR 0397078 |
| Reference:
|
[15] B. Malgrange: Ideals of differentiable functions.Oxford Univ. Press 1966. Zbl 0177.17902, MR 0212575 |
| Reference:
|
[16] J. E. Marsden M. McCrecken: The Hopf bifurcation and its applications.Springer Verlag, New York-Heidelberg-Berlin 1976. MR 0494309 |
| Reference:
|
[17] J. E. Marsden: Qualitative methods in bifurcation theory.Bull. Amer. Math. Soc., Vol. 84, No. 6 (1978), 1125-1148. Zbl 0404.35010, MR 0508450, 10.1090/S0002-9904-1978-14549-2 |
| Reference:
|
[18] J. G. Sinaj L. P. Šilnikov: Strange attractors.Proceedings, (Russian) Mir, Moscow 1981. MR 0624437 |
| Reference:
|
[19] F. Takens: Unfoldings of certain singularities of vector fields: Generalized Hopf bifurcation.J. Diff. Eq. 14 (1973), 476-493. MR 0339264, 10.1016/0022-0396(73)90062-4 |
| Reference:
|
[20] F. Takens: Forced oscillations.Notes, Ultrecht 1974. |
| Reference:
|
[21] Yung-Chen Lu: Singularity theory and an introduction to catastrophe theory.Springer Verlag, New York-Heidelberg-Berlin 1976. Zbl 0354.58008, MR 0461562 |
| . |
