  These notes describe some applications of the analysis of ordinary
differential equations to the study of the viscous approximation of
conservation laws in one space dimension. The exposition mostly focuses on the
analysis of invariant manifolds like the center manifold and the stable
manifold. The last section addresses a more specific issue and describes a
possible way of extending the notions of center and stable manifold to some
classes of singular ordinary differential equations arising in the study of the
Navier-Stokes equation in one space variable.
