  We show the existence of nonautonomous invariant manifolds for planar,
asymptotically autonomous differential equations, that have equilibrium
solutions with zero Lyapunov spectrum. These invariant manifolds correspond to
the stable and unstable manifold of a desingularized equation, that we obtain
by using the blow-up method. More precisely, the blow-up method is extended to
the nonautonomous setting and transforms the original finite-dimensional
ordinary differential equation into an infinite-dimensional delay equation with
infinite delay, but hyperbolic structure. In the technical construction of the
invariant manifolds for the delay equation, we have to carefully study the
effect of the time reparametrization used for desingularization in the blown-up
space to guarantee sufficient regularity. This allows us to employ a
Lyapunov-Perron argument to obtain existence of an invariant manifold. We
combine the last step with an implicit function argument to study
differentiability of the manifold. Finally, we reverse the blow-up
transformation of space and time variables obtaining invariant manifolds of the
initially considered equation.
