On the Stability of Equivariant Bifurcation Problems and Their Unfoldings
Canadian mathematical bulletin, Tome 35 (1992) no. 2, pp. 237-246

Voir la notice de l'article provenant de la source Cambridge University Press

In their book Singularities and Groups in Bifurcation Theory M. Golubitsky, I. Stewart and D. Schaeffer have introduced an equivariant version of Martinet's notion of V (for variety)-equivalence with parameter. In this paper we give a unified proof that, in this context, infinitesimal stability is equivalent to stability at the local level of germs and that stability in the unfolding category is equivalent to versality.
DOI : 10.4153/CMB-1992-034-x
Mots-clés : 58E07, 58C27
Lari-Lavassani, Ali; Lu, Yung-Chen. On the Stability of Equivariant Bifurcation Problems and Their Unfoldings. Canadian mathematical bulletin, Tome 35 (1992) no. 2, pp. 237-246. doi: 10.4153/CMB-1992-034-x
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[AGV, 1985] Arnold, V. I., Gusein-Zade, S. M., and Varchenko, A. N., Singularities of Differentiable Maps, 1 Birkhàuser, Basel/Stuttgart, (1985). Google Scholar

[B, 1977] Bierstone, E., Generic equivariant maps. Real and Complex Singularities, Sijthoff and Nordhoff, (1977), 127-161. Google Scholar

[B, 1980] Bierstone, E., The Structure of Orbit Spaces and the Singularities of Equivariant Mappings, Rio de Janeiro, 1980. Google Scholar

[D, 1984] Damon, J., The Unfolding and determinacy theorems for subgroups of Si and %_, Memoirs, A.M.S. , Providence, 1984. Google Scholar

[G, 1988] Gervais, J. J., Stability of Unfoldings in the Context of Equivariant Contact-Equivalence, Pacific Journal of Math. (2) 132(1988), 283–291. Google Scholar

[GSS, 1988] Golubitsky, M., Stewart, I., and Schaeffer, D. G., Singularities and Groups in Bifurcation Theory, 2, Springer, Berlin/Heidelberg/New York, 1988. Google Scholar

[1,1980] Izumiya, S., Stability of G-Unfoldings, Hokkaido Math. J. 9(1980), 36–45. Google Scholar

[L, 1990] Lari-Lavassani, A., Multiparameter Bifurcation With Symmetry Via Singularity Theory, Ph.D. Thesis, The Ohio State University, 1990. Google Scholar

[LL, 1990] Lari-Lavassani, A. and Lu, Y.-C., The Stability Theorem for Subgroups of SI and 3£, preprint, 1991. Google Scholar

[LL, 1991] Lari-Lavassani, A. and Lu, Y.-C., Equivariant Multiparameter Bifurcation Via Singularity Theory, preprint, 1991. Google Scholar

[M, 1975] Martinet, J., Déploiements versels des applications différentiables et classification des applicationsstables. In: Singularités d'Applications Différentiables, Plan-sur-Bex, Lecture Notes in Math. 535, Springer-Verlag, Berlin/Heidelberg/New York, (1975), 1–44. Google Scholar

[P, 1976] Poénaru, V., Singularités C°° en Présence de Symétrie, Lecture Notes in Math. , Springer-Verlag, Berlin/Heidelberg/New York, (1976). Google Scholar

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