Bifurcation problems with O(2)⊕Z2 symmetry and the buckling of a cylindrical shell

In this paper we employ equivariant singularity theory to study the postbuckling behavior of a cylindrical shell under axial compression, obtaining some results about the existence of secondary bifurcations and how they are connected to each other. The basic idea, first employed by Bauer, Keller and Reiss in [1], and then coupled with singularity theory by Schaeffer and Golubitsky in [16] and [17] and by Buzano in [4], consists in unfolding a multiple eigenvalue, obtained by forcing two eigenvalues to coalesce by varying the geometric parameters of the shell. This approah is made possible by a general analysis of bifurcation problems invariant with respect to the symmetries of the cylinder i.e. with respect to the group O(2)⊕Z2.