Preprint A224/2003
On the classification of analytic differential equations in $(\Bbb{C}^{2},0)$
Leonardo Câmara
Keywords: holomorphic foliations | holonomy | resolution of singularities
We study the classification of analytic differential equations in $(\Bbb{C}^{2},0)$. We give a complete set of analytic invariants determining the analytic type of the underling foliation. In particular we generalize some previous results about dicritical singularities in a straightforward manner. Such problem has its origins in a conjecture proposed by R. Thom in the middle 1970s.