Invariant foliations near normally hyperbolic equilibria for quasilinear   parabolic problems
  We consider quasilinear parabolic evolution equations in the situation where the set of equilibria forms a finite-dimensional C^1-manifold which is normally hyperbolic. The existence of foliations of the stable and unstable manifolds is shown assuming merely C^1-regularity of the underlying equation. 
Jan Pruess, Gieri Simonett, Mathias Wilke
math.AP math.DS