On the integrability of holomorphic vector fields
Leonardo Câmara Bruno Scárdua
Discrete & Continuous Dynamical Systems - A 2009, 25(2): 481-493 doi: 10.3934/dcds.2009.25.481
We determine topological and algebraic conditions for a germ of holomorphic foliation $\mathcal{F}_X$ induced by a generic vector field $X$ on $(\mathbb{C}^{3},0)$ to have a holomorphic first integral, i.e., a germ of holomorphic map $F$ : $(\mathbb{C}^{3},0)\rightarrow(\mathbb{C}^{2},0)$ such that the leaves of $\mathcal{F}_X$ are contained in the level curves of $F$.
keywords: maps tangent to the identity. holonomy groups First integrals

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