Differentiable equisingularity of holomorphic foliations
  We prove that a $C^{\infty}$ equivalence between germs holomorphic foliations at $({\mathbb C}^2,0)$ establishes a bijection between the sets of formal separatrices preserving equisingularity classes. As a consequence, if one of the foliations is of second type, so is the other and they are equisingular. 
Rog\'erio Mol and Rudy Rosas
math.DS