## Journals

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### Open Access Journals

DCDS

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
$F$.

DCDS

We study the geometrical and dynamical properties of a
holomorphic vector field on a complex surface, assumed to be
transverse to the boundary of a domain which is a non-smooth
manifold with boundary and corners. We obtain hyperbolicity and
prove a compact leaf result. For a pseudoconvex domain with
boundary diffeomorphic to the boundary of a bidisc in $\mathbb C^2$ the
foliation is pull-back of a liner hyperbolic foliation. If
moreover the diffeomorphism is transversely holomorphic then we
have linearization.

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