Abstract
We consider the class ν n of germs of holomorphic vector fields in (\(\mathbb{C}^2\), 0) with vanishing (n − 1)-jet at zero. We prove that the formal equivalence of two generic germs in ν n implies their analytic equivalence. This result is analogous to the one obtained in [16] for the case of orbital analytic equivalence.
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Ortiz-Bobadilla, L., Rosales-González, E. & Voronin, S.M. Rigidity Theorem for Degenerated Singular Points of Germs of Holomorphic Vector Fields in the Complex Plane. Journal of Dynamical and Control Systems 7, 553–599 (2001). https://doi.org/10.1023/A:1013110718209
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DOI: https://doi.org/10.1023/A:1013110718209