| Title:
|
Normal forms and bifurcations of some equivariant vector fields (English) |
| Author:
|
Medveď, Milan |
| Language:
|
English |
| Journal:
|
Mathematica Slovaca |
| ISSN:
|
0139-9918 |
| Volume:
|
40 |
| Issue:
|
2 |
| Year:
|
1990 |
| Pages:
|
209-223 |
| . |
| Category:
|
math |
| . |
| MSC:
|
37C80 |
| MSC:
|
37G05 |
| MSC:
|
37G99 |
| idZBL:
|
Zbl 0735.58024 |
| idMR:
|
MR1094774 |
| . |
| Date available:
|
2009-09-25T10:24:35Z |
| Last updated:
|
2012-08-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/129378 |
| . |
| Reference:
|
[1] BRÖCKER, Tһ., LANDER L.: Diffеrеntiablе Gеrms and Catastrophеs.Cambridgе Univеrsity Prеss 1975. |
| Reference:
|
[2] BUZANO E., GEYMONAT G., POSTON T.: Post buckling bеhaviour of a non-linеarly hypеrеlastic thin rod with crossеction invariant undеr thе dihеdral group Dn.Arch. Rational Mеch. Anal. 89, 1985, 307-388. MR 0792535 |
| Reference:
|
[3] CARR J.: Applications of Cеntеr Manifold Thеory.Appl. Math. Sci. 35, Springеr-Vеrlag 1981. MR 0635782 |
| Reference:
|
[4] CUSHMAN R., SANDERS J. A.: Nilpotеnt normal forms and rеprеsеntation thеory of sl(2. R)+.Multiparamеtеr bifurcation thеory, procееdings, еd. M. Golubitsky and J. Guckеnhеimеr, AMS sеriеs: Contеmporary Math., Vol. 56, 1986, 31-51. MR 0855083 |
| Reference:
|
[5] DANGELMAYR G., GUCKENHEIMER J.: On a four paramеatеr family of planar vеctor fiеlds.Archivе for Rational Mеch. Anal. Vol. 97, 1987, p. 321. MR 0865844 |
| Reference:
|
[6] ELPHICK C., TIRAPEGNI E., BRACHET M., COULLET P., IOOSS G.: A simplе global characterization of normal forms of singular vector fields.Preprint No. 109, University of Nice 1986; in Physica 29D, 1987, 95-127. MR 0923885 |
| Reference:
|
[7] FIEDLER B.: Global Bifurcation of Periodic Solutions with Symmetry.Lecture notes in Math. 1309, Springer-Verlag, Heidelberg 1988. Zbl 0644.34038, MR 0947144 |
| Reference:
|
[8] GOLUBITSKY M., ROBERTS M.: A classification of degenerate Hopf bifurcations with 0(2) symmetry.J. Diff.Eq. 69 1987, 216-264. MR 0899161 |
| Reference:
|
[9] GOLUBITSKY M., SCHAEFFER D. G.: Singularities and Groups in Bifurcation Theory.Vol. I, Applied Math. Sciences 51, Springer-Verlag, New York, 1985. Zbl 0607.35004, MR 0771477 |
| Reference:
|
[10] GOLUBITSKY M., STEWART I.: Hopf bifurcation in the presence of symmetry.Archive for Rational Mech. and Analysis, Vol. 87, No. 2, 1985, 107-165. Zbl 0588.34030, MR 0765596 |
| Reference:
|
[11] GUCKENHEIMER J.: A codimension two bifurcation with circular symmetry.Multiparameter bifurcation theory, AMS series: Contemporary Math., Vol. 56, 1986, 175-184. Zbl 0616.58034, MR 0855089 |
| Reference:
|
[12] GUCKENHEIMER J., HOLMES P.: Nonlinear Oscillations.Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York 1983. Zbl 0515.34001, MR 0709768 |
| Reference:
|
[13] KLÍČ A.: Period doubling bifurcations in a two-box model of the Brusselator.Aplikace matematiky, Vol. 28, No. 5, 1983, 335-343. Zbl 0531.34030, MR 0712910 |
| Reference:
|
[14] KLÍČ A.: Bifurcations of the periodic solutions in symmetric systems.Aplikace matematiky, Vol. 31,No. 1, 1986, 27-40. Zbl 0596.34024, MR 0836800 |
| Reference:
|
[15] MEDVEĎ M.: The unfoldings of a germ of vector fìelds in the plane with a singularity of codimension 3.Czech. Math. J., Vol. 35, No. 1, 1985, 1-42. Zbl 0591.58022, MR 0779333 |
| Reference:
|
[16] SATTINGER D. H.: Group Theoretical Methods in Bifurcation Theory.Lecture Notes in Math. 762, Springer-Verlag, Berlin 1979. |
| Reference:
|
[17] TAKENS F.: Forced oscillations and bifurcation.Comm. Math. Inst. Rijksuniversitait Ultrecht 3, 1974, 1-59. MR 0478235 |
| Reference:
|
[18] VANDERBAUWHEDE A.: Center manifolds, normal forms and elementary bifurcations.to appear in Dynamics Reported. MR 1000977 |
| Reference:
|
[19] VANDERBAUWHEDE A.: local Bifurcation and Symmetry.Pitman, Boston 1982. Zbl 0539.58022, MR 0697724 |
| Reference:
|
[20] VANDERBAUWHEDE A.: Hopf bifurcation at non-semisimple eigenvalues.Multiparameter bifurcation theory, AMS series: Contemporary Math., Vol. 56, 1986, 343-353. Zbl 0607.58031, MR 0855101 |
| Reference:
|
[21] VANDERBAUWHEDE A.: Secondary bifurcations of periodic solutions in autonomous systems.Canadian mathemataical Society, Conference Proceedings, Vol. 3, 1987, 693-701. Zbl 0629.34051, MR 0909945 |
| . |
