Analytic classification of saddle nodes

S. M. Voronin, Yu. I. Meshcheryakova
2005 Transactions of the Moscow Mathematical Society  
Isolated degenerate elementary singular points (saddle nodes) of germs of holomorphic vector fields in (C 2 , 0) are studied. An analytic classification of them is obtained; it is shown that the analytic classification has two times more moduli (numeric and functional) than the orbital analytic classification. A theorem on sectorial normalization is proved.
doi:10.1090/s0077-1554-05-00151-2 fatcat:qros7mosgzhmjb2o5xlcrydhlm