Title:  On the unfolding of singularity of reversible vector fields with 
        SO(2) symmetry and non-semisimple eigenvalue 0

Speaker: Andrei Afendikov, Moscow

Reversible $SO(2)$-invariant vector fields in $\R^4$ depending on
parameters appear in a variety of physical applications. If the involution
commutes with the action of the symmetry group then quasihomogeneous
truncation corresponding to a positive face of the Newton polyhedra of the
problem after the appropriate scaling yields stationary complex
Ginzburg-Landau equation (cGL). In multiparameter problems degenerate
(e.g. cubic-quintic) cGL appear. For truncated problem explicit
expressions for  $SO(2)$-orbits of homoclinic solutions are known to
exist. The aim of the work is to relate these solutions to homoclinic
solutions of the original problem and to study the dynamics in a vicinity
of these solutions. For instance the existence of cascades of homoclinic
to $0$  $2^n3^l$-pulse solutions is demonstrated.