Normal forms and bifurcations of some equivariant vector fields

 Access to full text

 Full (PDF)

1. BRÖCKER, Tһ., LANDER L., Diffеrеntiablе Gеrms and Catastrophеs, Cambridgе Univеrsity Prеss 1975. (1975) 
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. (1985) MR0792535
3. CARR J., Applications of Cеntеr Manifold Thеory, Appl. Math. Sci. 35, Springеr-Vеrlag 1981. (1981) MR0635782
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. (1986) MR0855083
5. DANGELMAYR G., GUCKENHEIMER J., On a four paramеatеr family of planar vеctor fiеlds, Archivе for Rational Mеch. Anal. Vol. 97, 1987, p. 321. (1987) MR0865844
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. (1986) MR0923885
7. FIEDLER B., Global Bifurcation of Periodic Solutions with Symmetry, Lecture notes in Math. 1309, Springer-Verlag, Heidelberg 1988. (1988) Zbl0644.34038MR0947144
8. GOLUBITSKY M., ROBERTS M., A classification of degenerate Hopf bifurcations with 0(2) symmetry, J. Diff.Eq. 69 1987, 216-264. (1987) MR0899161
9. GOLUBITSKY M., SCHAEFFER D. G., Singularities and Groups in Bifurcation Theory, Vol. I, Applied Math. Sciences 51, Springer-Verlag, New York, 1985. (1985) Zbl0607.35004MR0771477
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. (1985) Zbl0588.34030MR0765596
11. GUCKENHEIMER J., A codimension two bifurcation with circular symmetry, Multiparameter bifurcation theory, AMS series: Contemporary Math., Vol. 56, 1986, 175-184. (1986) Zbl0616.58034MR0855089
12. GUCKENHEIMER J., HOLMES P., Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields, Springer-Verlag, New York 1983. (1983) Zbl0515.34001MR0709768
13. KLÍČ A., Period doubling bifurcations in a two-box model of the Brusselator, Aplikace matematiky, Vol. 28, No. 5, 1983, 335-343. (1983) Zbl0531.34030MR0712910
14. KLÍČ A., Bifurcations of the periodic solutions in symmetric systems, Aplikace matematiky, Vol. 31,No. 1, 1986, 27-40. (1986) Zbl0596.34024MR0836800
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. (1985) Zbl0591.58022MR0779333
16. SATTINGER D. H., Group Theoretical Methods in Bifurcation Theory, Lecture Notes in Math. 762, Springer-Verlag, Berlin 1979. (1979) 
17. TAKENS F., Forced oscillations and bifurcation, Comm. Math. Inst. Rijksuniversitait Ultrecht 3, 1974, 1-59. (1974) MR0478235
18. VANDERBAUWHEDE A., Center manifolds, normal forms and elementary bifurcations, to appear in Dynamics Reported. MR1000977
19. VANDERBAUWHEDE A., local Bifurcation and Symmetry, Pitman, Boston 1982. (1982) Zbl0539.58022MR0697724
20. VANDERBAUWHEDE A., Hopf bifurcation at non-semisimple eigenvalues, Multiparameter bifurcation theory, AMS series: Contemporary Math., Vol. 56, 1986, 343-353. (1986) Zbl0607.58031MR0855101
21. VANDERBAUWHEDE A., Secondary bifurcations of periodic solutions in autonomous systems, Canadian mathemataical Society, Conference Proceedings, Vol. 3, 1987, 693-701. (1987) Zbl0629.34051MR0909945

1. Milan Medveď, On a codimension 3 bifurcation of plane vector fields with $Z_2$ symmetry