Dynamic bifurcation of the complex Swift-Hohenberg equation (Q1030555)

This paper deals with attractor bifurcations in the complex Swift--Hohenberg equation under Dirichlet and periodic boundary conditions. In particular, it is shown that the trivial solution bifurcates to a non-trivial finite-dimensional attractor (the dimension of which depends on the boundary conditions and the eigenvalues of the linearization). The proofs in the paper are based on both center manifold and Lyapunov--Schmidt reduction.