  We are interested in a complete characterization of the contact-line
singularity of thin-film flows for zero and nonzero contact angles. By treating
the model problem of source-type self-similar solutions, we demonstrate that
this singularity can be understood by the study of invariant manifolds of a
suitable dynamical system. In particular, we prove regularity results for
singular expansions near the contact line for a wide class of mobility
exponents and for zero and nonzero dynamic contact angles. Key points are the
reduction to center manifolds and identifying resonance conditions at
equilibrium points. The results are extended to radially-symmetric source-type
solutions in higher dimensions. Furthermore, we give dynamical systems proofs
for the existence and uniqueness of self-similar droplet solutions in the
nonzero dynamic contact-angle case.
