| Title:
|
On a codimension 3 bifurcation of plane vector fields with $Z_2$ symmetry (English) |
| Author:
|
Medveď, Milan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1990 |
| Pages:
|
295-310 |
| . |
| Category:
|
math |
| . |
| MSC:
|
34C05 |
| MSC:
|
34C23 |
| MSC:
|
58F14 |
| idZBL:
|
Zbl 0724.34014 |
| idMR:
|
MR1046295 |
| DOI:
|
10.21136/CMJ.1990.102381 |
| . |
| Date available:
|
2008-06-09T15:32:55Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/102381 |
| . |
| Reference:
|
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| Reference:
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[2] N. N. Bautin, E. A. Leontovich: Methods and Examples of Qualitative Study of Dynamical Systems in the Plane.Nauka, Moscow 1978 (Russian). |
| Reference:
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[3] R. I. Bogdanov: Versal deformations of a singular point of vector fields in the plane in the case of zero eigenvalues.Selecta Math. Soviet 1 (1981), 389-421 (Proc. of Petrovski Seminar, 2 (1976), 37-65) (Russian). MR 0442996 |
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[4] R. I. Bogdanov: Bifurcations of limit cycles of a certain family of vector fields in the plane.Selecta Math. Soviet 1 (1981), 373-387 (Proc. of Petrovski Seminar 2 (1976), 23-36) (Russian). MR 0442988 |
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[7] S. N. Chow, J. K. Hale: Methods of Bifurcation Theory.Springer-Verlag, New York 1982. Zbl 0487.47039, MR 0660633 |
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[8] S. N. Chow, J. A. Sanders: On the number of critical points of the period.J. Differential Equations 64 (1986), 51-66. Zbl 0594.34028, MR 0849664, 10.1016/0022-0396(86)90071-9 |
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[9] R. Cushman, J. A. Sanders: A codimension two bifurcation with a third-order Picard-Fuchs equation.J. Differential Equations 59 (1985), 243 - 256. Zbl 0571.34021, MR 0804890, 10.1016/0022-0396(85)90156-1 |
| Reference:
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[10] G. Dangelmayer, J. Guckenheimer: On a four parameter family of plane vector fields.Archive for Rational Mechanics and Analysis, 97 (1987), 321 - 352. MR 0865844, 10.1007/BF00280410 |
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[11] B. Drachman S. A. Van Gils, Zhang Zhi-Fen: Abelian integrals for quadratic vector fields.J. Reine Angew. Math. 382 (1987), 165-180. MR 0921170 |
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[12] F. Dumortier R. Roussarie, J Sotomayor: Generic 3-parameter families of vector fields on the plane.Unfolding a singularity with nilpotent linear part. The cusp-case of codimension 3, Ergodic Theory Dynamical Systems 7 (1987), No. 3, 375-413. MR 0912375 |
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[13] C. Elpic E. Tirapegni M. Brachet P. Coullet, G. Iooss: A simple global characterization of normal forms of singular vector fields.Preprint No. 109, University of Nice, 1986, Physica 29 D (1987), 95-127. MR 0923885 |
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[14] J. Guckenheimer: Multiple bifurcation problems for chemical reactors.Physica 20 D (1986), 1-20. Zbl 0593.34043, MR 0858791 |
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[15] J. Guckenheimer: A condimension two bifurcation with circular symmetry.in "Multiparameter Bifurcation Theory", AMS series: Contemporary Math. 56 (1986), 175-184. MR 0855089 |
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[16] J. Guckenheimer, P. Holmes: Nonlinear Oscillations.Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York 1983. Zbl 0515.34001, MR 0709768 |
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[17] E. I. Horozov: Versal deformation of equivariant vector fields with $Z_2$ or $Z_3$ symmetry.Proc. of Petrovski Seminar 5 (1979), 163-192 (Russian). MR 0549627 |
| Reference:
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[18] J. K. Hale: Introduction to dynamic bifurcation.in "Bifurcation Theory and Applications" (L. Salvadoei, Ed.), pp. 106-151, LNM 1057, Springer-Verlag 1984. Zbl 0544.58016, MR 0753299 |
| Reference:
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[19] Yu. S. Ilyashenko: Multiplicity of limit cycles arising from perturbations of the form $w' = = P_2/Q_1$ of a Hamiltonian equation in the real and complex domain.Amer. Math. Soc. Transl. Vol. 118, No. 2, pp. 191-202, AMS, Providence, R. I., 1982. 10.1090/trans2/118/10 |
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[20] Yu. S. Ilyashenko: Zeros of special abelian integrals in a real domain.Funct. Anal. Appl. 11 (1977), 309-311. |
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[21] M. Medved: Generic bifurcations of vector fields with a singularity of codimension 2.in "Equadiff 5, Bratislava 1981", Proceedings, Teubner-Texte zur Math., Band 47, Teubner-Verlag 1982, pp. 260-263. MR 0715987 |
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[22] M. Medved: The unfoldings of a germ of vector fields in the plane with a singularity of codimension 3.Czechosl. Math. J. 35 (110), 1 (1985), 1-42. Zbl 0591.58022, MR 0779333 |
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[23] M. Medved: Normal forms and bifurcations of some equivariant vector fields.to appear in Mathematica Slovaca 1990. Zbl 0735.58024, MR 1094774 |
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| . |
