## Journals

- Advances in Mathematics of Communications
- Big Data & Information Analytics
- Communications on Pure & Applied Analysis
- Discrete & Continuous Dynamical Systems - A
- Discrete & Continuous Dynamical Systems - B
- Discrete & Continuous Dynamical Systems - S
- Evolution Equations & Control Theory
- Inverse Problems & Imaging
- Journal of Computational Dynamics
- Journal of Dynamics & Games
- Journal of Geometric Mechanics
- Journal of Industrial & Management Optimization
- Journal of Modern Dynamics
- Kinetic & Related Models
- Mathematical Biosciences & Engineering
- Mathematical Control & Related Fields
- Mathematical Foundations of Computing
- Networks & Heterogeneous Media
- Numerical Algebra, Control & Optimization
- Electronic Research Announcements
- Conference Publications
- AIMS Mathematics

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.

## Year of publication

## Related Authors

## Related Keywords

[Back to Top]